Gravitational wave snapshots of generic extreme mass ratio inspirals

Scott A. Hughes; Steve Drasco

REVIEW

Gravitational wave snapshots of generic extreme mass ratio inspirals

Steve Drasco, Scott A. Hughes

General Relativity and Quantum Cosmology · Submitted 26 Sep 2005 · 70 references

Pith's verdict: The first Teukolsky calculation for Kerr orbits that are eccentric and inclined at once — solid machinery, honest about its limits, but the advertised 10^-3 accuracy is a limit-case number, not a generic-orbit number.

T0 · AI review

How this review was made: An AI referee (selfhosted/deepseek-v4.1-flash) read the paper on October 29, 2026 and answered a fixed list of questions about it. T0 is the starting level every paper gets. The levels describe how deeply Pith has checked the paper, never the authors.

T0 AI review An AI read the paper and answered a fixed list of questions.
T1 Audit Automatic checks that the references and files the paper relies on exist and match.
T2 Compute The paper's code or calculations re-run with the same results.
T3 Formal statement The claims written out in a formal math language a computer can read.
T4 Proof Those claims proved, and the proof checked by computer.

How Pith checks papers →

· 3 major objections · 10 minor · Ask about this paper · The compiled record · Read the full review →

Challenge this review Comment (0) Read on arXiv ↗

Cite ▾

arXiv IDgr-qc/0509101 (version 2)

Pith ID4HIGXVZL, Pith's permanent record of this paper and its review

CitationScott A. Hughes, Steve Drasco. "Gravitational wave snapshots of generic extreme mass ratio inspirals." arXiv:gr-qc/0509101 (2005). https://pith.science/paper/4HIGXVZL

Cite this reviewBibTeX for Pith's review of this paper

Claim paper

Why Pith says this

Highlight any text to comment on it.

Editor's note

read the letter

Bottom line: this fills the last row of the paper's own Table I — first Teukolsky-based waveforms and radiative fluxes for Kerr orbits that are simultaneously eccentric and inclined. The machinery is standard and the bookkeeping is careful. The thing to know before you quote the numbers is that the accuracy claims are validated at the edges of parameter space, not in the middle of it. The stress-test note on this point lands, and I'd weigh it in how you cite the fluxes rather than in whether the paper is worth reading. It is. The geodesic frequency-domain expansions are efficient and clean, the source construction from the exact geodesic is done properly, and the Sasaki-Nakamura step for numerical stability is the right call. Validation is real: 10^-5 against the circular code, 10^-3 against Glampedakis-Kennefick, the Schwarzschild Wigner-D identity at 10^-5, and post-Newtonian agreement at roughly 10^-3. The authors also report, rather than bury, a factor-of-three disagreement with Glampedakis-Kennefick on one horizon energy flux, sign flip included. That is the behaviour you want from a code paper. The soft spots are proportionate. Every external cross-check switches off one generic ingredient — circular tests inclination at e=0, equatorial tests eccentricity at theta_inc=0, the PN comparison is a small-eccentricity, small-inclination expansion. The genuinely new corner (a=0.9M, e~0.5-0.7, theta_inc~60-80 deg) rests on internal convergence between eps_flux=10^-4 and 10^-3, and the brackets in Tables VI-VII degrade to 10^-2 and 10^-1 there. That is self-consistency, not independent validation, and the failure mode is silent because both runs share the same hand-tuned mode-zeroing threshold. The authors call that threshold 'unacceptable' for production use, which is the right word. The unexplained horizon-flux disagreement is a smaller issue since the total flux is infinity-dominated, but it is a published physical quantity and deserves a sentence of diagnosis. The 'voices' are a relabeling of the (k,n) indices, not new dynamics, but the empirical claim that the radial voice dominates by e~0.3-0.5 is checkable and useful. Who should read it: anyone building Teukolsky codes or scoping EMRI data-analysis waveforms. Not measurement templates, and the paper says so. Send it out; ask for a clearer statement of where the accuracy brackets actually hold.

Referee report

Significance

This is the first calculation of gravitational waves and radiative fluxes for generic (eccentric and inclined) bound Kerr orbits, filling the last cell of Table I and completing a program that had previously been restricted to circular or equatorial orbits. The result matters: astrophysical EMRIs are expected to be both eccentric and inclined, so the previous specializations were not adequate even for data-analysis development. The voice decomposition is a genuinely useful diagnostic that organizes the waveform phenomenology by orbital parameter, and the observation that the azimuthal voice alone can carry most of the power at low eccentricity has practical consequences for cheap waveform generation. The validation against two independent codes, and against an exact symmetry identity, is a real strength and is reported with appropriate quantitative care. The authors are also candid about the two load-bearing approximations (neglect of the conservative self force; the dQ/dt ansatz of Eq. (3.62)), which is to their credit.

Major objections (3)

[Sec. IV D and Tables VI-VII] The external validation does not cover the regime that is the paper's actual deliverable. Every cross-check sits at an edge of parameter space where one generic ingredient is switched off: Ref. [1] tests inclination at e = 0, Ref. [2] tests eccentricity at theta_inc = 0, and the post-Newtonian comparison of Ref. [70] is a small-eccentricity, small-inclination expansion. The one exact identity verified, Eq. (4.15), is checked only for Schwarzschild orbits. Consequently the accuracy of the fluxes in the genuinely new corner (a = 0.9M, e ~ 0.5-0.7, theta_inc ~ 60-80 deg) rests entirely on the internal convergence test, i.e. comparing the same flux computed at requested epsilon_flux = 1e-4 and 1e-3. That is self-consistency, not independent validation. The brackets in Tables VI-VII make the point concretely: the e = 0.7, theta_inc = 80 deg, p = 6 row quotes [1e-1] for <dE/dt>_infinity and [1e-1] for <dLz/dt>_infinity, and several e = 0.7 rows quote [1e-2]. The authors should state explicitly, in the conclusions and not only in the table captions, that the generic-corner fluxes carry at most one to two significant figures, and should identify which entries in Tables VI-VII should not be used at face value. A short paragraph explaining what drives the [1e-1] entry specifically (radial-index truncation, the zeroing threshold, or the dynamic accuracy control of Sec. IV B) would materially help the reader judge which catalog rows are trustworthy.
[Sec. IV D, horizon flux comparison] The disagreement with Glampedakis and Kennefick on the horizon energy flux is reported but left entirely undiagnosed: typically 1-10%, and in one case (e = 0.4, p = 5 in Table VII of Ref. [2]) a factor of about three with opposite sign. The authors correctly note that the total flux is dominated by the infinity contribution, so the paper's headline numbers are unaffected. But the horizon flux is one of the two quantities the paper claims to deliver, and a factor-of-three sign disagreement with a published code is a correctness risk for that quantity, not merely a cosmetic discrepancy. At minimum the authors should say which computation they believe is correct and why, and should suggest a concrete discriminating test. Two candidates are worth naming: the near-horizon coefficient alpha_lmkn of Eq. (3.60), whose |C_lmkn|^2 expression (3.61) is intricate and is exactly the kind of place a sign or factor error would hide; and the behavior of the horizon flux in the limit of modes with small P = omega - m a/(2 M r_+), where the alpha factor becomes small and the two codes could plausibly diverge. If the authors have already checked either, saying so would close the issue.
[Sec. IV B, mode-zeroing threshold and Psi-star tuning] The paper's stated purpose (Sec. VI) is to feed an adiabatic inspiral code, and the authors themselves call the hand-tuning of the mode-zeroing threshold 'unacceptable' for such a code. That acknowledgment is appropriate, but it leaves a reproducibility gap in the present manuscript: the threshold is described only qualitatively ('the ratio of the magnitude of the integral Z to the maximum over zeta and chi of the absolute value of the integrand'), and the authors note it had to be re-tuned 'particularly as we explored orbits with increasing eccentricity'. Likewise the Psi-star constants of Eq. (3.49) are described as tuned per mode, decreasing with l and e, without a stated rule. As a result a reader cannot reproduce Tables VI-VII from the text alone. The authors should either tabulate the threshold and Psi-star values actually used for the catalog of Table III, or state the tuning rule explicitly enough to be reimplemented. This is a modest request and would substantially raise the value of the paper as infrastructure.

Minor objections (10)

[Tables VI-VII] The <dQ/dt> column is computed from the inclination-preserving ansatz of Eq. (3.62), which the authors rightly call a speculation, yet it is printed to the same number of digits and in the same visual register as fluxes quoted at 1e-4. The caption does say the accuracy is unknown, but a reader skimming the tables will not register the distinction. Consider separating the column typographically or moving it to its own table.
[Fig. 4 and Fig. 6 captions] Both captions state 'aM = 0.9M^2', which is dimensionally inconsistent; the intended statement is a = 0.9M (or a/M = 0.9). The same slip appears in the Fig. 4 caption text as 'aM = 0.9M 2'.
[Sec. II, Eq. (2.12)] The second relation reads 'theta(-w_theta) = r(w_theta)'; the right-hand side should be theta(w_theta).
[Appendix A, Eq. (A6) and following note] Eq. (A6) defines z_- = cos^2 theta_min, but the footnote immediately after Eq. (A11) says 'Schmidt defines z_- as cos theta_min [45]'. These two statements are inconsistent as written; presumably the footnote means Schmidt uses a different symbol or a different normalization. Please reconcile.
[Sec. V B] The sentence 'for orbits with eccentricity as low as 0.1 and inclinations theta_inc <~ 45 deg or theta_inc /greaterorsimilar 135 deg' contains a garbled relational symbol that should be typeset as a proper inequality.
[Table I] The checkmark layout is difficult to parse: the column headers ('a != 0', 'eccentric orbits', 'inclined orbits', 'evolve orbits') do not align unambiguously with the marks, and the first data row is rendered as 'Ref. a != 0 eccentric orbits...'. A cleaner table, with an explicit column for 'fluxes computed' versus 'inspiral evolved', would make the historical summary much more useful.
[Sec. IV C, Eq. (4.13)] The fitting formula for the peak radial index is quoted without stating the range of e over which the fit was performed or its residuals. Since this formula is proposed as the seed for a future truncation scheme, its domain of validity should be stated.
[Sec. V A] The suggestion that H ~ H_radial might suffice for some applications is left qualitative. A single number, e.g. the fraction of the total flux or a waveform mismatch for the e = 0.5, theta_inc = 45 deg case of Table II, would let the reader judge whether the approximation is worth pursuing.
[Fig. 5 caption] The caption refers to 'Eq. (5.6a)' for the separated pieces, but the separation is defined across Eqs. (5.5)-(5.6d); cite the range.
[References] Ref. [68] reads 'Phys. Ref. D 58, 064012 (1998)'; this should be Phys. Rev. D. There are also several typographical artifacts in the body text ('Techno logy', 'arbitary', 'properites', 'pratical', 'preceed', 'homogenenous', 'Kinnersly' for Kinnersley) that should be cleaned up in proof.

How Pith checks papers → · Full audit of this paper →

The paper

The paper claims

The paper computes gravitational waves from a test mass on any bound orbit around a spinning black hole, eccentric and tilted at once, and splits the radiation into separable 'voices' tied to the orbit's three frequencies.

The reading

Extreme mass ratio inspirals — a stellar-mass compact object spiralling into a massive black hole — are prime targets for a space-based gravitational-wave detector, but modelling their waves requires knowing what a small body on a generic orbit radiates. Earlier calculations handled only circular orbits or orbits confined to the black hole's equatorial plane. This paper removes both restrictions: it solves the Teukolsky equation for a spinless test particle on a bound Kerr geodesic that is simultaneously eccentric and inclined, and it extracts the energy and axial angular momentum carried to infinity and down the event horizon. The authors' framing device is that the wave can be read as a chorus of 'voices', each labelled by integer harmonics $(k,n)$ of the polar and radial orbital frequencies, so that varying eccentricity and inclination turns individual voices up or down. The payoff, if the machinery holds, is a cheap way to build approximate inspiral waveforms for developing detection algorithms, not a template accurate enough for final parameter measurement.

What carries the argument

The load-bearing mechanism is the frequency-domain Teukolsky–Sasaki–Nakamura pipeline: the Weyl scalar $ψ_4$ is separated into spin-weighted spheroidal harmonics and radial functions, the radial equation is solved in an 'in-up' basis constructed via the Sasaki–Nakamura transformation to avoid the numerical swamping of ingoing by outgoing amplitudes, and the inhomogeneous solution is assembled from Green's-function integrals over a source term built from the particle's energy-momentum tensor projected onto the Kinnersley tetrad. The second piece of machinery is the biperiodic expansion of the geodesic source: because $r(λ)$ and $θ(λ)$ are periodic and even under the chosen fiducial initial conditions, the source integrals become two-dimensional Fourier sums over $(k,n)$, turning an integral over frequency into a discrete sum. The third piece is the truncation scheme, which decides how many $(l,m,k,n)$ terms to keep by monitoring convergence of the fluxes themselves, with buffer counts of 2 in $k$ and 5 in $n$ and a hand-tuned threshold for discarding modes that have bottomed out into numerical noise.

Extended reading notes

Core claim

The central claim is that black-hole perturbation theory, pushed through the Teukolsky equation with a source built from the exact geodesic worldline, delivers the gravitational waves and the radiative fluxes of energy and axial angular momentum for a spinless test mass on any bound geodesic of a Kerr black hole — eccentric and inclined at the same time. Because the orbit's radial and polar motions are periodic in Mino time, the source can be expanded in a discrete set of frequencies $ω_{mkn} = mΩ_φ + kΩ_θ + nΩ_r$, and each mode $(l,m,k,n)$ is computed independently. Grouping modes by which frequency they oscillate at gives the 'voices': the azimuthal voice ($k=n=0$), the polar voice ($n=0$, $k≠0$), the radial voice ($k=0$, $n≠0$), and a mixed remainder. The authors report that the radial voice generally dominates once eccentricity reaches roughly $e≈0.3$–$0.5$, that the polar voice can be made dominant only at low eccentricity and high inclination, and that for low-eccentricity orbits near the equatorial plane the azimuthal voice alone carries over half the power — a large practical saving, since it collapses the four-dimensional mode sum to two dimensions. The paper also reports flux tables across a catalogue of orbits with $a=0.9M$, together with a Carter-constant evolution rate obtained by assuming radiation leaves the orbital inclination unchanged.

Load-bearing premise

The reported fluxes are only as good as the rule that decides when to stop adding modes: the sums over the radial index $n$ follow no general decay pattern, and the threshold for discarding modes that have sunk into numerical noise had to be tuned by hand.

Editorial extensions

If this is right

Coupling these snapshot fluxes to a prescription for the radiative evolution of the Carter constant would let a sequence of geodesics be stitched into an adiabatic inspiral for generic, non-equatorial, eccentric orbits.
Because the azimuthal voice alone can carry most of the radiated power at low eccentricity and near-equatorial inclination, cheap two-dimensional mode sums may suffice for some detection-template applications.
The mode amplitudes are independent, so the calculation parallelises almost perfectly across processors, making large catalogues of orbits tractable.
The published flux tables for $a=0.9M$ orbits give a benchmark against which independent codes — time-domain evolution, post-Newtonian expansions, or self-force calculations — can be checked.
The voice decomposition suggests that detection schemes might target the loudest voices of a signal rather than needing to model the full chorus.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

The voice structure looks like a natural handle for data analysis: if the radial voice dominates at moderate eccentricity, a search could be staged, first matching a radial-voice template and only later refining with the full mode set.
The disagreement with the equatorial code on horizon energy fluxes — up to a factor of three in one case, with opposite signs — is a concrete loose end that an independent time-domain calculation could settle, and it would tell us whether the horizon contribution is being computed correctly at all.
The assumption that radiation does not change orbital inclination, used to get $\langle dQ/dt \rangle$, is the weakest link in the eventual inspiral chain; a self-force calculation of the true Carter-constant evolution for a few generic orbits would test it directly.
Since the mode sums are truncated by a hand-tuned rule that the authors call unacceptable for production, an untruncated or adaptively truncated recomputation of one high-eccentricity case would quantify how much flux might be hiding in uncomputed modes.

Original abstract

Using black hole perturbation theory, we calculate the gravitational waves produced by test particles moving on bound geodesic orbits about rotating black holes. The orbits we consider are generic - simultaneously eccentric and inclined. The waves can be described as having radial, polar, and azimuthal "voices", each of which can be made to dominate by varying eccentricity and inclination. Although each voice is generally apparent in the waveform, the radial voice is prone to overpowering the others. We also compute the radiative fluxes of energy and axial angular momentum at infinity and through the event horizon. These fluxes, coupled to a prescription for the radiative evolution of the Carter constant, will be used in future work to adiabatically evolve through a sequence of generic orbits. This will enable the calculation of inspiral waveforms that, while lacking certain important features, will approximate those expected from astrophysical extreme mass ratio captures sufficiently well to aid development of measurement algorithms on a relatively short timescale.

The compiled record

The paper's own sentences, arranged, kept beside the review and separate from it. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.

Compiled by classifier-1.13-20260917 via OpenRouter, question bank abstract-p1-20260923, 2026-09-23: 1 request, 5,573 input tokens, $0.0002 reported.

What the abstract itself states, as probabilities: claims first 0.04 · states limitation 0.94 · human participants 0.01 · controlled comparison 0.02 · randomized assignment 0.01 · states quantitative result 0.05 · compares with prior results 0.09 · mentions code or data availability 0.02.

The abstract, sentence by sentence

arXiv listing abstract v2. Results and the main claim are underlined; show every role.

Using black hole perturbation theory, we calculate the gravitational waves produced by test particles moving on bound geodesic orbits about rotating black holes. The orbits we consider are generic - simultaneously eccentric and inclined. The waves can be described as having radial, polar, and azimuthal "voices", each of which can be made to dominate by varying eccentricity and inclination. Although each voice is generally apparent in the waveform, the radial voice is prone to overpowering the others. We also compute the radiative fluxes of energy and axial angular momentum at infinity and through the event horizon. These fluxes, coupled to a prescription for the radiative evolution of the Carter constant, will be used in future work to adiabatically evolve through a sequence of generic orbits. This will enable the calculation of inspiral waveforms that, while lacking certain important features, will approximate those expected from astrophysical extreme mass ratio captures sufficiently well to aid development of measurement algorithms on a relatively short timescale.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#	sentence	role	the authors' own work	states the main conclusion	strength
s0	Using black hole perturbation theory, we calculate the gravitational waves produced by test particles moving on bound geodesic orbits about rotating black holes.	method 0.54	0.96	0.06	asserted 1.00
s1	The orbits we consider are generic - simultaneously eccentric and inclined.	contribution 0.92	0.68	0.04	asserted 1.00
s2	The waves can be described as having radial, polar, and azimuthal "voices", each of which can be made to dominate by varying eccentricity and inclination.	result 0.94	0.85	0.18	asserted 0.84
s3	Although each voice is generally apparent in the waveform, the radial voice is prone to overpowering the others.	result 0.90	0.85	0.14	asserted 0.80
s4	We also compute the radiative fluxes of energy and axial angular momentum at infinity and through the event horizon.	result 0.51	0.96	0.05	asserted 1.00
s5	These fluxes, coupled to a prescription for the radiative evolution of the Carter constant, will be used in future work to adiabatically evolve through a sequence of generic orbits.	future work 1.00	0.48	0.10	asserted 0.70
s6	This will enable the calculation of inspiral waveforms that, while lacking certain important features, will approximate those expected from astrophysical extreme mass ratio captures sufficiently well to aid development of measurement algorithms on a relatively short timescale.	future work 0.88	0.15	0.37	hedged possibility 0.62

What kind of paper the classifier reports this is: theoretical result 0.51 · evidence from simulation or computation 0.91.

What was examined, and what was not

sources read

arXiv listing abstract v2

not examined

full text
figures and tables
references and citing sentences
relations to other papers

levels run

P abstract

not run

S sections
T body sentences
C citations
R cross-paper relations

Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

Figures

**Figure 1.** FIG. 1: The orbital torus and the evolution of

**Figure 2.** FIG. 2: Modal energy flux through the horizon (superscript

**Figure 3.** FIG. 3: Modal energy flux through the horizon (superscript

**Figure 4.** FIG. 4: A comparison of waveforms associated with a generic

**Figure 5.** FIG. 5: The waveform from Fig. 4 and its separated pieces

**Figure 6.** FIG. 6: Snapshot waveforms for orbits with inclination

Figures reproduced from arXiv:gr-qc/0509101 by the authors.

References

Works cited (70)

[1]

S. A. Hughes, Evolution of circular, nonequatorial or- bits of Kerr black holes due to gravitational-wave emis- sion, Phys. Rev. D 61, 084004 (2000); Phys. Rev. D 63, 049902(E) (2001); Phys. Rev. D 65, 069902(E) (2002); Phys. Rev. D 67, 089901(E) (2003)

View on Pith 2000
[2]

K. Glampedakis and D. Kenneﬁck, Zoom and whirl: Eccentric equatorial orbits around spinning black holes and their evolution under gravitational radiation reac- tion, Phys. Rev. D 66, 044002 (2002)

View on Pith 2002
[70]

N. Sago, T. Tanaka, W. Hikida, H. Nakano, K. Ganz, The adiabatic evolution of orbital parameters in the Kerr spacetime, gr-qc/0511151

View on Pith Pith review arXiv
[3]

C. W. Misner, K. S. Thorne, and J. A. Wheeler, Gravi- tation (Freeman, San Francisco, 1973)

View on Pith 1973
[4]

B. Carter, Global structure of the Kerr family of gravita- tional ﬁelds , Phys. Rev. 174, 1559 (1968)

View on Pith 1968
[5]

Y. Mino, Perturbative approach to an orbital evolution around a supermassive black hole , Phys. Rev. D 67, 084027 (2003)

View on Pith 2003
[6]

S. A. Hughes, S. Drasco, ´E. ´E. Flanagan, and J. Franklin, Gravitational radiation reaction and inspiral waveforms in the adiabatic limit , Phys. Rev. Lett. 94, 221101 (2005)

View on Pith 2005
[7]

S. Drasco, ´E. ´E. Flanagan, and S. A. Hughes, Computing inspirals in Kerr in the adiabatic regime. I. The scalar case, Class. Quantum Grav. 22, S801 (2005)

View on Pith 2005
[8]

N. Sago, T. Tanaka, W. Hikida, and H. Nakano, Adiabatic radiation reaction to the orbits in Kerr Spacetime , Prog. Theor. Phys., in press; gr-qc/0506092

View on Pith Pith review arXiv
[9]

L. Ferrarese and D. Merritt, A Fundamental Relation be- 27 tween Supermassive Black Holes and Their Host Galax- ies, Astrophys. J. 539, L9 (2000)

View on Pith 2000
[10]

K. Gebhardt et al, A Relationship between Nuclear Black Hole Mass and Galaxy Velocity Dispersion , Astrophys. J. 539, L13 (2000)

View on Pith 2000
[11]

L. Spitzer, Equipartition and the Formation of Compact Nuclei in Spherical Stellar Systems , Astrophys. J. 158, L139 (1969)

View on Pith 1969
[12]

J. Miralda-Escud´ e and A. Gould, A Cluster of Black Holes at the Galactic Center , Astrophys. J. 545, 847 (2000)

View on Pith 2000
[13]

M. P. Muno, E. Pfahl, F. K. Baganoﬀ, W., N. Brandt, A. Ghez, J. Lu, and M. R. Morris, An Overabundance of Transient X-Ray Binaries within 1 Parsec of the Galactic Center, Astrophys. J. 622, L113 (2005)

View on Pith 2005
[14]

M. Freitag, Monte Carlo cluster simulations to determine the rate of compact star inspiralling to a central galactic black hole , Class. Quantum Grav. 18, 4033 (2001)

View on Pith 2001
[15]

See the oﬃcial NASA website http://lisa.nasa.gov

View on Pith
[16]

See the oﬃcial ESA website http://sci.esa.int/science-e/www/area/index.cfm?fareaid=27

View on Pith
[17]

J. R. Gair et al, Event rate estimates for LISA extreme mass ratio capture sources , Class. Quantum Grav. 21, S1595 (2004)

View on Pith 2004
[18]

L. Barack and C. Cutler, LISA Capture Sources: Ap- proximate Waveforms, Signal-to-Noise Ratios, and Pa- rameter Estimation Accuracy , Phys. Rev. D 69, 082005 (2004)

View on Pith 2004
[19]

F. D. Ryan, Gravitational waves from the inspiral of a compact object into a massive, axisymmetric body with arbitrary multipole moments , Phys. Rev. D 52, 5707 (1995)

View on Pith 1995
[20]

F. D. Ryan, Accuracy of estimating the multipole mo- ments of a massive body from the gravitational waves of a binary inspiral , Phys. Rev. D 56, 1845 (1997)

View on Pith 1997
[21]

N. A. Collins and S. A. Hughes, Towards a formalism for mapping the spacetimes of massive compact objects: Bumpy black holes and their orbits , Phys. Rev. D 69, 124022 (2004)

View on Pith 2004
[22]

S. A. Teukolsky, Rotating Black Holes: Separable Wave Equations for Gravitational and Electromagnetic Per- turbations, Phys. Rev. Lett. 29, 1114 (1972); S. A. Teukolsky, Perturbations of a rotating black hole. I. fundamental equations for gravitational, electromagneti c, and neutrino-ﬁeld perturbations , Astrophys. J. 185, 635 (1973)

View on Pith 1972
[23]

M. P. Ryan, Teukolsky equation and Penrose wave equa- tion, Phys. Rev. D 10, 1736 (1974)

View on Pith 1974
[24]

R. Penrose, A spinor approach to general relativity , Ann. Phys. (N.Y.) 10, 171 (1960)

View on Pith 1960
[25]

S. W. Hawking and J. B. Hartle, Energy and angular momentum ﬂow into a black hole , Commun. Math. Phys. 27, 283 (1972)

View on Pith 1972
[26]

J. B. Hartle, Tidal Friction in Slowly Rotating Black Holes Phys. Rev. D 8, 1010 (1973); Tidal shapes and shifts on rotating black holes 9, 2749 (1974)

View on Pith 1973
[27]

C. Gundlach, R. H. Price, and J. Pullin, Late-time be- havior of stellar collapse and explosions. I. Linearized perturbations, Phys. Rev. D 49, 883 (1994); Late-time behavior of stellar collapse and explosions. II. Nonlinear evolution, 49, 890 (1994)

View on Pith 1994
[28]

C. O. Lousto and R. H. Price, Head-on collisions of black holes: The particle limit , Phys. Rev. D 55, 2124 (1997)

View on Pith 1997
[29]

K. Martel, Gravitational waveforms from a point particle orbiting a Schwarzschild black hole , Phys. Rev. D 69, 044025 (2004)

View on Pith 2004
[30]

K. Martel and E. Poisson, One-parameter family of time- symmetric initial data for the radial infall of a particle into a Schwarzschild black hole , Phys. Rev. D 66, 084001 (2002)

View on Pith 2002
[31]

C. F. Sopuerta, P. Sun, P. Laguna, and J. Xu, A Toy Model for Testing Finite Element Methods to Simulate Extreme-Mass-Ratio-Binary Systems, gr-qc/0507112

View on Pith Pith review arXiv
[32]

C. Cutler, D. Kenneﬁck, and E. Poisson, Gravita- tional radiation reaction for bound motion around a Schwarzschild black hole , Phys. Rev. D 50, 3816 (1994)

View on Pith 1994
[33]

L. S. Finn and K. S. Thorne, Gravitational waves from a compact star in a circular, inspiral orbit, in the equatoria l plane of a massive, spinning black hole, as observed by LISA, Phys. Rev. D 62, 124021 (2000)

View on Pith 2000
[34]

M. Shibata, Gravitational waves induced by a particle or- biting around a rotating black hole , Prog. Theor. Phys. 90, 595 (1993)

View on Pith 1993
[35]

M. Shibata, Gravitational waves by compact stars orbit- ing around rotating supermassive black holes , Phys. Rev. D 50, 6297 (1994)

View on Pith 1994
[36]

S. A. Hughes, Evolution of circular, nonequatorial orbits of Kerr black holes due to gravitational-wave emission. II. Inspiral trajectories and gravitational waveforms , Phys. Rev. D 64, 064004 (2001)

View on Pith 2001
[37]

E. Poisson, An introduction to the Lorentz-Dirac equa- tion, gr-qc/9912045

View on Pith Pith review arXiv
[38]

P. A. M. Dirac, Classical theory of radiating electrons , Proc. R. Soc. London A167, 148 (1938)

View on Pith 1938
[39]

Y. Mino, M. Sasaki, and T. Tanaka, Gravitational radia- tion reaction to a particle motion , Phys. Rev. D 55, 3457 (1997)

View on Pith 1997
[40]

T. C. Quinn and R. M. Wald, Axiomatic approach to elec- tromagnetic and gravitational radiation reaction of parti - cles in curved spacetime , Phys. Rev. D 56, 3381 (1997)

View on Pith 1997
[41]

E. Poisson, The Motion of Point Particles in Curved Spacetime, Living Rev. Relativity 7, 6 (2004), http://www.livingreviews.org/lrr-2004-6

View on Pith 2004
[42]

A good summary of the current state and recent progress of this ﬁeld can be found in a special issue of the journal Classical and Quantum Gravity: Gravitational radiation from binary black holes: Advances in the perturbative ap- proach, edited by C. O. Lousto; Class. Quantum Grav. 22, number 15 (2005) (Institute of Physics Publishing, Bristol, 2005)

View on Pith 2005
[43]

A. Pound, E. Poisson, and B. G. Nickel, Limitations of the adiabatic approximation to the gravitational self-for ce, Phys. Rev. D 72, 124001 (2005)

View on Pith 2005
[44]

S. Drasco and S. A. Hughes, Rotating black hole orbit functionals in the frequency domain , Phys. Rev. D 69, 044015 (2004)

View on Pith 2004
[45]

W. Schmidt, Celestial mechanics in Kerr spacetime , Class. Quant. Grav. 19, 2743 (2002)

View on Pith 2002
[46]

M. Sasaki and T. Nakamura, Gravitational radiation from a Kerr black hole. I , Prog. Theor. Phys. 67, 1788 (1982)

View on Pith 1982
[47]

D. C. Wilkins, Bound Geodesics in the Kerr Metric , Phys. Rev. D 5, 814 (1972)

View on Pith 1972
[48]

R. H. Boyer and R. W. Lindquist, Maximal Analytic Ex- tension of the Kerr Metric , J. Math. Phys. 8, 265 (1967)

View on Pith 1967
[49]

R. M. Wald, On perturbations of a Kerr black hole , J. Math. Phys. 14, 1453 (1973). 28

View on Pith 1973
[50]

E. Newman and R. Penrose, An approach to Gravita- tional Radiation by a Method of Spin Coeﬃcients , J. Math. Phys. 3, 566 (1962)

View on Pith 1962
[51]

S. Chandrasekhar, The Mathematical Theory of Black Holes (Oxford University Press, New York, 1983)

View on Pith 1983
[52]

E. Poisson, Absorption of mass and angular momentum by a black hole: Time-domain formalisms for gravita- tional perturbations, and the small-hole/slow-motion ap- proximation, Phys. Rev. D 70, 084044 (2004)

View on Pith 2004
[53]

G. Khanna, Teukolsky evolution of particle orbits around Kerr black holes in the time domain: Elliptic and inclined orbits, Phys. Rev. D 69, 024016 (2004)

View on Pith 2004
[54]

R. Fujita and H. Tagoshi, New Numerical Methods to Evaluate Homogeneous Solutions of the Teukolsky Equa- tion, Prog. Theor. Phys. 112, 415 (2004)

View on Pith 2004
[55]

G. Arfken, Mathematical Methods for Physicists (third edition, Academic Press, Orlando, FL, 1985)

View on Pith 1985
[56]

R. A. Breuer, Gravitational Perturbation Theory and Synchrotron Radiation, Lecture Notes in Physics Vol. 44 (Springer-Verlag, Berlin, 1975)

View on Pith 1975
[57]

M. Sasaki and H. Tagoshi, Analytic Black Hole Perturbation Approach to Gravitational Ra- diation, Living Rev. Relativity 6, 6 (2003), http://www.livingreviews.org/lrr-2003-6/

View on Pith 2003
[58]

W. Kinnersly, Type D Vacuum Metrics , J. Math. Phys. 10, 1195 (1969)

View on Pith 1969
[59]

Y. Mino et al., Black hole perturbation , Prog. Theor. Phys. Suppl. 128, 1 (1997)

View on Pith 1997
[60]

R. D. Blandford and K. S. Thorne, Applications of Classical Physics , unpublished book, available at http://www.pma.caltech.edu/Courses/ph136/yr2004/, Chapt. 26

View on Pith
[61]

R. A. Isaacson, Gravitational Radiation in the Limit of High Frequency. II. Nonlinear Terms and the Eﬀective Stress Tensor, Phys. Rev. 166, 1272 (1968)

View on Pith 1968
[62]

S. A. Teukolsky and W. H. Press, Perturbations of Rotat- ing Black Hole. III. Interaction of the Hole with Gravita- tional and Electromagnetic Radiation , Astrophys. J. 193, 443 (1974)

View on Pith 1974
[63]

C. Cutler, private communication

View on Pith
[64]

J. Gair, private communication

View on Pith
[65]

W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical Recipes in C++: The Art of Sci- entiﬁc Computing (Cambridge University Press, Cam- bridge, 2002)

View on Pith 2002
[66]

P. C. Peters and J. Mathews, Gravitational Radiation from Point Masses in a Keplerian Orbit , Phys. Rev. 131, 435 (1963)

View on Pith 1963
[67]

K. S. Thorne, Multipole Expansions of Gravitational Ra- diation, Rev. Mod. Phys. 52, 299 (1980)

View on Pith 1980
[68]

D. Kenneﬁck, Stability under radiation reaction of circu- lar equatorial orbits around Kerr black holes , Phys. Ref. D 58, 064012 (1998)

View on Pith 1998
[69]

M. Shibata and K. Glampedakis, private communica- tions

View on Pith

Forward citations

Cited by 34 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

The shape of nonlinearity in binary-black-hole dynamics
gr-qc 2026-10 accept novelty 7.0 of 10

The paper identifies the dominant sources of discrepancy between black-hole perturbation theory and numerical relativity across the waveform, showing that inspiral errors are largely dissipative, precessing systems ha...
Spectral suppression of black hole ringdown tails
gr-qc 2026-06 unverdicted novelty 7.0 of 10

Spectral properties of oscillatory sources suppress the branch-cut contribution to black hole ringdown tails, explaining their absence in quasi-circular mergers.
Analytical Fluxes from Generic Schwarzschild Geodesics
gr-qc 2026-05 unverdicted novelty 7.0 of 10

An analytic Chebyshev-expansion method computes gravitational-wave fluxes from arbitrary-eccentricity Schwarzschild geodesics by reducing them to sums of prior Keplerian Fourier coefficients, with numerical tests show...
Gravitational radiation from Kerr black holes using the Sasaki-Nakamura formalism: Waveforms and fluxes at infinity
gr-qc 2025-11 conditional novelty 7.0 of 10

A new integration-by-parts scheme computes Sasaki-Nakamura waveforms directly from the Teukolsky source term, bypassing the standard extra radial integration for bound orbits.
Post-adiabatic dynamics and waveform generation in self-force theory: an invariant pseudo-Hamiltonian framework
gr-qc 2025-07 conditional novelty 7.0 of 10

A pseudo-Hamiltonian reformulation of 1PA self-force dynamics yields local, invariant action-angle evolution equations and an embedded conservative Hamiltonian whose on-shell energy equals the first-law binding energy.

Show 29 more citing papers

Metric reconstruction and the Hamiltonian for eccentric, precessing binaries in the small-mass-ratio limit
gr-qc 2025-07 conditional novelty 7.0 of 10

First-order metric perturbations and the generalized redshift invariant are computed for eccentric, precessing orbits in Kerr spacetime using four metric reconstruction methods, with open-source code provided.
Gravitational waves from b-EMRIs: Doppler shift and beaming, resonant excitation, helicity oscillations and self-lensing
gr-qc 2025-06 conditional novelty 7.0 of 10

A first-principles Teukolsky model of a binary extreme-mass-ratio inspiral shows Doppler modulation, beaming, self-lensing, helicity-dependent scattering, and SMBH ringdown resonances in the waveform.
Approach to the separatrix with eccentric orbits
gr-qc 2024-12 conditional novelty 7.0 of 10

The adiabatic inspiral near the separatrix for eccentric orbits is solved analytically, with the Lambert W_{-1} function controlling the late-time decay of the distance to the separatrix.
Post-Newtonian expansion of gravitational energy and angular momentum fluxes: inclined spherical orbits about a Kerr black hole
gr-qc 2024-11 conditional novelty 7.0 of 10

The paper derives 12PN flux formulas for inclined spherical Kerr orbits, exact in spin and inclination.
Gravitational self-force on generic bound geodesics in Kerr spacetime
gr-qc 2017-11 conditional novelty 7.0 of 10

First numerical calculation of the gravitational self-force on generic eccentric, inclined bound geodesics in Kerr spacetime, validated against analytic regularization parameters and the flux balance law.
EMRIs in Kerr Spacetime: The Role of Inclination Diffusion
astro-ph.GA 2026-10 accept novelty 6.0 of 10

Inclination diffusion from two-body scattering in Kerr spacetime increases the EMRI-to-plunge ratio, yielding a factor of ~2.5 rate enhancement for spinning black holes and a similar factor for relativistic vs. Newton...
Gravitational-wave signatures of spinning particles around rotating hairy black holes
gr-qc 2026-10 conditional novelty 6.0 of 10

For a rotating gravitational-decoupling hairy black hole, the main waveform signature of both secondary spin and hair is accumulated dephasing, and the hair's radial reach, not its amplitude, controls how distinguisha...
Unified remnant models for aligned-spin, precessing, and eccentric binary black hole mergers
gr-qc 2026-08 conditional novelty 6.0 of 10

New analytic fits, gwModelRemS/P, predict remnant mass, spin, luminosity, and kick for black hole mergers from equal mass to q=1000, with a neural-flow model for precessing kicks.
Spin-Hair Induced Chaos of Spinning Test Particles in Rotating Hairy Black Holes
gr-qc 2026-05 unverdicted novelty 6.0 of 10

Spinning test particles around rotating hairy black holes show finite-time instability in localized regions of the (spin, hair-parameter) plane that reorganize the strong-field phase space compared to Kerr.
Efficient and stable computation of gravitational-wave fluxes from generic Kerr orbits via a unified Heun-function framework
gr-qc 2026-05 unverdicted novelty 6.0 of 10

A unified confluent HeunC framework with hybrid connection-coefficient computation and adaptive bi-power quadrature yields relative errors of order 10^{-11} and 2-10x speedups over existing packages for total radiativ...
Advancing the Effective-One-Body Framework in the Test-Mass Limit
gr-qc 2026-03 conditional novelty 6.0 of 10

SEOB-TML cuts dephasing by up to an order of magnitude in the test-mass limit by Q-factorizing the flux (including horizon absorption) and by modeling mode mixing with extracted QNM coefficients.
Observable signature of magnetic tidal coupling in hierarchical triple systems
gr-qc 2025-10 conditional novelty 6.0 of 10

Magnetic tidal fields from a supermassive black hole trigger new orbital resonances in a companion compact binary, boosting eccentricity and altering its gravitational-wave signal.
Consistency of spin effects between numerical relativity and perturbation theory for inspiraling comparable-mass black hole binaries
gr-qc 2025-10 conditional novelty 6.0 of 10

Adiabatic point-particle black hole perturbation theory reproduces numerical-relativity spin effects in comparable-mass inspirals to within ~1%, so only small spin-dependent post-adiabatic corrections are needed.
Resonant interactions from dynamical perturbers on generic orbits around an extreme mass ratio inspiral
gr-qc 2025-07 conditional novelty 6.0 of 10

A numerical scan of 141,130 third-body resonances in EMRI systems finds no action changes above 1% but some waveform phase shifts near 0.1 radian.
Post-Newtonian templates for phase evolution of spherical extreme mass ratio inspirals
gr-qc 2024-11 conditional novelty 6.0 of 10

A 12PN analytic phase model for quasi-spherical inclined EMRIs in Kerr spacetime is presented, and TaylorT1 is found to converge fastest among the time-domain approximants.
Adiabatic waveforms for extreme mass-ratio inspirals via multivoice decomposition in time and frequency
gr-qc 2021-02 conditional novelty 6.0 of 10

Splitting an extreme mass-ratio inspiral waveform into slowly evolving 'voices' lets a long strong-field waveform be stitched together from precomputed single-orbit snapshots, in both the time and frequency domains.
Black hole perturbation theory and gravitational self-force
gr-qc 2021-01 conditional novelty 6.0 of 10

The paper provides a unified review and a new multiscale framework for generating post-adiabatic gravitational waveforms from generic nonresonant orbits around Kerr black holes.
Deep-Learning-Assisted Bayesian Inference for Extreme-Mass-Ratio Inspirals
gr-qc 2026-11 conditional novelty 5.0 of 10

A deep-learning-assisted Bayesian inference framework for EMRI parameter estimation that combines neural-network-guided search-space reduction, particle swarm optimization, and staged MCMC sampling, demonstrated on no...
Periodic orbits and gravitational-wave emission from extreme-mass-ratio inspirals around rotating charged black holes in nonlinear electrodynamics
gr-qc 2026-10 accept novelty 5.0 of 10

A systematic study of periodic orbits and gravitational-wave emissions from extreme-mass-ratio inspirals around rotating charged black holes in Einstein-Euler-Heisenberg nonlinear electrodynamics shows that larger spi...
Periodic orbits and their gravitational waves in EMRIs: supermassive black hole affected by galactic dark matter halos
gr-qc 2025-10 conditional novelty 5.0 of 10

Periodic zoom-whirl orbits and their gravitational waveforms in NFW, Beta, and Moore dark matter halos deviate from Schwarzschild predictions by an amount set by halo mass and radius, with NFW and Beta nearly identica...
Tidal heating as a discriminator for horizons in extreme mass ratio inspirals
gr-qc 2019-10 conditional novelty 5.0 of 10

Absence of a black-hole horizon in an extreme-mass-ratio inspiral shifts the gravitational-wave phase by 10^2 to 10^4 radians, enough for LISA to bound the central object's reflectivity below 0.01 percent.
Fast Self-forced Inspirals
gr-qc 2018-02 conditional novelty 5.0 of 10

Near-identity averaging transformations reduce self-force inspiral equations to phase-independent form, cutting trajectory computation from hours to milliseconds while staying within the accuracy of the underlying sel...
Foundations of an effective-one-body model for coalescing binaries on eccentric orbits
gr-qc 2017-07 conditional novelty 5.0 of 10

The authors recast effective-one-body binary dynamics in orbital-geometry variables and fundamental frequencies, deriving eccentric evolution equations and 1.5PN fluxes that reproduce known post-Newtonian results in t...
Extreme Mass-Ratio Inspirals in the Effective-One-Body Approach: Quasi-Circular, Equatorial Orbits around a Spinning Black Hole
gr-qc 2010-09 conditional novelty 5.0 of 10

An effective-one-body waveform model, calibrated with eight fitted coefficients against Teukolsky fluxes, tracks Teukolsky-based EMRI waveforms to better than one radian of phase over 2 to 6 months for circular equato...
Distinguishing scale-dependent Planck stars from renormalization group improved Schwarzschild black holes by Gravitational waves
gr-qc 2025-06 conditional novelty 4.0 of 10

Gravitational-wave strains from analytic-kludge EMRI models can distinguish scale-dependent Planck stars from renormalization-group improved Schwarzschild black holes, at least for the chosen orbit parameters.
Gravitational self force in extreme mass-ratio inspirals
gr-qc 2009-08 accept novelty 4.0 of 10

The review organizes gravitational self-force methods for extreme mass-ratio inspirals and gives the first detailed derivation of the Kerr mode-sum regularization parameters.
Rational Orbits and Gravitational-Wave Signatures around a Horndeski Black Hole
gr-qc 2026-11 conditional novelty 3.0 of 10

Bound geodesics around a static Horndeski black hole shift outward and their periodic-orbit parameter q changes as the effective hair parameter p_eff increases, with approximate quadrupole gravitational-wave strains r...
Self-force and radiation reaction in general relativity
gr-qc 2018-05 accept novelty 3.0 of 10

Gravitational self-force calculations now connect to post-Newtonian and numerical-relativity results and are being folded into a single waveform model intended to cover all black-hole mass ratios.
Testing General Relativity with Low-Frequency, Space-Based Gravitational-Wave Detectors
gr-qc 2012-12 accept novelty 3.0 of 10

A structured survey of the general-relativity tests that low-frequency space-based gravitational-wave detectors could perform, with quantitative projections for each test and explicit caveats about the modeling those ...

How later papers used it

113 later papers cite it

Evidence: substantial. 97 of the citing papers share no author with it, and 31 of those carry a confident label from Pith's citation classifier.

Pith read 10 of the 188 citing sentences, choosing only those whose citation markers point at this paper alone, and wrote the paraphrases from them. The summary, the counts, the evidence level, the links and the quotes come from code; the summary counts the papers listed below. A later paper is listed under a label when Pith's citation classifier gives one of its sentences that label at probability 0.8 or more (0.95 for support), Pith's reading finds that the citing paper itself did it, and a second check confirms the paraphrase against the sentence. This section lists uses only. It does not list criticism or disagreement, so their absence here says nothing about how the paper has been received. Papers that share an author with this one are listed apart, under "By the same authors". A quote is the citing authors' own sentence, shown when their paper's licence is CC BY, CC BY-SA or CC0. JSON

3 later papers by other authors are listed below: 2 used its method or tool and 1 cited it as support. 1 more paper by the same authors is listed: 1 used its method or tool.

Uses its method or tool 3 of 34 papers with this label · 1 by the same authors

Replaced the integrals for the coefficients of the inhomogeneous solutions with suitable integrals over the orbital torus described by q_r and q_z as per this paper.

Gravitational self-force on eccentric equatorial orbits around a Kerr black hole (2016) · 0.88 · paraphrased: the licence does not allow quoting
Adopted this paper's dynamic mode-truncation scheme to guarantee convergence at high eccentricities.

Pitching Cosmic Curveballs: Environmental Effects on Extreme-Mass-Ratio Inspirals with Spinning Secondaries (2026) · 1.00 · paraphrased: the licence does not allow quoting

By the same authors

Followed a similar procedure to this paper to prove that the amplitudes can be written as a sum over discrete frequencies.

Asymptotic gravitational-wave fluxes from a spinning test body on generic orbits around a Kerr black hole (2023) (same authors) · 0.97 · paraphrased: the licence does not allow quoting

Cites it as support 1 of 4 papers with this label

Said that its conclusion that Mino's scheme has severe limitations was supported by a recent analysis by this paper.

Multi-scale analysis of the electromagnetic self-force in a weak gravitational field (2007) · 1.00 · paraphrased: the licence does not allow quoting

How the literature uses it

97 arXiv papers cite this in 162 sentences

Each citing sentence is taken from the citing paper's LaTeX source and typed by Pith's classifier. A label appears at probability 0.8 or more (0.95 for support), a contest at 0.7 or more; the quoted words are the citing authors'. How each label was checked · JSON

Papers citing it · 94 sentences without a confident label

Builds on it 1 paper

Besides taking into account statistical correlations as discussed above, our analysis should be extended to retrograde or inclined orbits, exploiting previous self-force calculations for scalar charges on generic trajectories [ref] , to the case of an (ultralight) massive scalar field (see [ref] ), and to theories with multiple fields and couplings constants.

Extreme mass-ratio inspirals as probes of scalar fields: eccentric equatorial orbits around Kerr black holes · Conclusions · 0.81

Uses its method or tool 28 papers

Our adiabatic ppBHPT waveforms are simulated using the time-domain inspiral-merger-ringdown Teukolsky solver developed in Refs. [ref] where the radiative energy and angular momentum losses are computed with the open-source code GremlinEq [ref] .

Consistency of spin effects between numerical relativity and perturbation theory for inspiraling comparable-mass black hole binaries · Introduction · 1.00
Therefore, to overcome this problem, in the equations of motion for the orbital dynamics of the plunging particle, we employ the energy flux computed by a highly-accurate frequency-domain Teukolsky code [ref] .

Small mass plunging into a Kerr black hole: Anatomy of the inspiral-merger-ringdown waveforms · Introduction · 0.99
The expression for change in action due to the self-force, $J_sf,i$ is given in Equation (12) of [ref] , or following the logic in Equations (22–24) of [ref] : [equation] where the sum is over all the modes and the angular quantum number $l$, and $α_ lm$ is the normalization factor for energy absorbed by the black hole [ref] .

Resonant interactions from dynamical perturbers on generic orbits around an extreme mass ratio inspiral · Simulating orbits: adiabatic evolution · 0.84

Uses its data or values 1 paper

[ref] also indicate that the size of the first term in the series is less than unity, and in fact of order $κ_1∼λ_1∼0.1$.

Transition of EMRIs through resonance: corrections to higher order in the on-resonance flux modification · Regime and domain of the variables · 0.97

Compares with it 1 paper

This comparison covers the full extent of the Toolkit’s available data—up to the innermost stable circular orbit (ISCO)—which was produced in Refs. [ref] .

Advancing the Effective-One-Body Framework in the Test-Mass Limit · Numerical dynamics computation · 0.94

Cites it as support 4 papers

This conclusion was supported by a recent analysis by Drasco and Hughes [ref] , and the general attitude currently is that while the radiative approximation may be useful to generate template waveforms for signal detection, it is probably insufficient for reliable parameter estimation.

Multi-scale analysis of the electromagnetic self-force in a weak gravitational field · Introduction · 1.00
Scaling with $e_0$— For the Kerr$ℓ$2 model, as the eccentricity increases, higher $ℓ$-mode amplitudes are no longer suppressed in general, and are more similar in magnitude to the $ℓ= 2$ mode (cf. Refs. [ref] .) This leads to worsened parameter recovery with the Kerr$ℓ$2 model.

The Fast and the Frame-Dragging: Efficient waveforms for asymmetric-mass eccentric equatorial inspirals into rapidly-spinning black holes · Results 1: Sigma contour levels · 0.96
This condition must be satisfied for three consecutive modes, because the modes are not monotonic in $n$, as has been reported already in other papers [ref] .

Adiabatic equatorial inspirals of a spinning body into a Kerr black hole · Gravitational-wave fluxes · 0.96

Cites it as background 28 papers

Each mode is indexed by integers $(ℓ, m, n, k)$, where $(ℓ, m)$ label the spin-weighted spheroidal harmonics, and the harmonic numbers $(n, k)$ correspond to the radial and polar motions [ref] .

A Deep Learning Framework for Amplitude Generation of Generic EMRIs · Adiabatic inspiral waveform construction · 0.91
On the other hand, the BHPT framework linearizes the Einstein equation, treating smaller black hole to be a point particle [ref] .

Mapping between black-hole perturbation theory and numerical relativity II: gravitational-wave momentum · Introduction · 0.95
The waveform at infinity could be obtained from the Teukolsky equations [ref] in time or in frequency domain [ref] .

EMRI data analysis with a phenomenological waveform · Review of EMRI waveforms · 0.93

Discussion

Disagree with the review, or know something it missed? Leave a comment, highlight any passage above to comment on it, or challenge this review formally.

[1] [1]

S. A. Hughes, Evolution of circular, nonequatorial or- bits of Kerr black holes due to gravitational-wave emis- sion, Phys. Rev. D 61, 084004 (2000); Phys. Rev. D 63, 049902(E) (2001); Phys. Rev. D 65, 069902(E) (2002); Phys. Rev. D 67, 089901(E) (2003)

View on Pith 2000

[2] [2]

K. Glampedakis and D. Kenneﬁck, Zoom and whirl: Eccentric equatorial orbits around spinning black holes and their evolution under gravitational radiation reac- tion, Phys. Rev. D 66, 044002 (2002)

View on Pith 2002

[3] [70]

N. Sago, T. Tanaka, W. Hikida, H. Nakano, K. Ganz, The adiabatic evolution of orbital parameters in the Kerr spacetime, gr-qc/0511151

View on Pith Pith review arXiv

[4] [3]

C. W. Misner, K. S. Thorne, and J. A. Wheeler, Gravi- tation (Freeman, San Francisco, 1973)

View on Pith 1973

[5] [4]

B. Carter, Global structure of the Kerr family of gravita- tional ﬁelds , Phys. Rev. 174, 1559 (1968)

View on Pith 1968

[6] [5]

Y. Mino, Perturbative approach to an orbital evolution around a supermassive black hole , Phys. Rev. D 67, 084027 (2003)

View on Pith 2003

[7] [6]

S. A. Hughes, S. Drasco, ´E. ´E. Flanagan, and J. Franklin, Gravitational radiation reaction and inspiral waveforms in the adiabatic limit , Phys. Rev. Lett. 94, 221101 (2005)

View on Pith 2005

[8] [7]

S. Drasco, ´E. ´E. Flanagan, and S. A. Hughes, Computing inspirals in Kerr in the adiabatic regime. I. The scalar case, Class. Quantum Grav. 22, S801 (2005)

View on Pith 2005

[9] [8]

N. Sago, T. Tanaka, W. Hikida, and H. Nakano, Adiabatic radiation reaction to the orbits in Kerr Spacetime , Prog. Theor. Phys., in press; gr-qc/0506092

View on Pith Pith review arXiv

[10] [9]

L. Ferrarese and D. Merritt, A Fundamental Relation be- 27 tween Supermassive Black Holes and Their Host Galax- ies, Astrophys. J. 539, L9 (2000)

View on Pith 2000

[11] [10]

K. Gebhardt et al, A Relationship between Nuclear Black Hole Mass and Galaxy Velocity Dispersion , Astrophys. J. 539, L13 (2000)

View on Pith 2000

[12] [11]

L. Spitzer, Equipartition and the Formation of Compact Nuclei in Spherical Stellar Systems , Astrophys. J. 158, L139 (1969)

View on Pith 1969

[13] [12]

J. Miralda-Escud´ e and A. Gould, A Cluster of Black Holes at the Galactic Center , Astrophys. J. 545, 847 (2000)

View on Pith 2000

[14] [13]

M. P. Muno, E. Pfahl, F. K. Baganoﬀ, W., N. Brandt, A. Ghez, J. Lu, and M. R. Morris, An Overabundance of Transient X-Ray Binaries within 1 Parsec of the Galactic Center, Astrophys. J. 622, L113 (2005)

View on Pith 2005

[15] [14]

M. Freitag, Monte Carlo cluster simulations to determine the rate of compact star inspiralling to a central galactic black hole , Class. Quantum Grav. 18, 4033 (2001)

View on Pith 2001

[16] [15]

See the oﬃcial NASA website http://lisa.nasa.gov

View on Pith

[17] [16]

See the oﬃcial ESA website http://sci.esa.int/science-e/www/area/index.cfm?fareaid=27

View on Pith

[18] [17]

J. R. Gair et al, Event rate estimates for LISA extreme mass ratio capture sources , Class. Quantum Grav. 21, S1595 (2004)

View on Pith 2004

[19] [18]

L. Barack and C. Cutler, LISA Capture Sources: Ap- proximate Waveforms, Signal-to-Noise Ratios, and Pa- rameter Estimation Accuracy , Phys. Rev. D 69, 082005 (2004)

View on Pith 2004

[20] [19]

F. D. Ryan, Gravitational waves from the inspiral of a compact object into a massive, axisymmetric body with arbitrary multipole moments , Phys. Rev. D 52, 5707 (1995)

View on Pith 1995

[21] [20]

F. D. Ryan, Accuracy of estimating the multipole mo- ments of a massive body from the gravitational waves of a binary inspiral , Phys. Rev. D 56, 1845 (1997)

View on Pith 1997

[22] [21]

N. A. Collins and S. A. Hughes, Towards a formalism for mapping the spacetimes of massive compact objects: Bumpy black holes and their orbits , Phys. Rev. D 69, 124022 (2004)

View on Pith 2004

[23] [22]

S. A. Teukolsky, Rotating Black Holes: Separable Wave Equations for Gravitational and Electromagnetic Per- turbations, Phys. Rev. Lett. 29, 1114 (1972); S. A. Teukolsky, Perturbations of a rotating black hole. I. fundamental equations for gravitational, electromagneti c, and neutrino-ﬁeld perturbations , Astrophys. J. 185, 635 (1973)

View on Pith 1972

[24] [23]

M. P. Ryan, Teukolsky equation and Penrose wave equa- tion, Phys. Rev. D 10, 1736 (1974)

View on Pith 1974

[25] [24]

R. Penrose, A spinor approach to general relativity , Ann. Phys. (N.Y.) 10, 171 (1960)

View on Pith 1960

[26] [25]

S. W. Hawking and J. B. Hartle, Energy and angular momentum ﬂow into a black hole , Commun. Math. Phys. 27, 283 (1972)

View on Pith 1972

[27] [26]

J. B. Hartle, Tidal Friction in Slowly Rotating Black Holes Phys. Rev. D 8, 1010 (1973); Tidal shapes and shifts on rotating black holes 9, 2749 (1974)

View on Pith 1973

[28] [27]

C. Gundlach, R. H. Price, and J. Pullin, Late-time be- havior of stellar collapse and explosions. I. Linearized perturbations, Phys. Rev. D 49, 883 (1994); Late-time behavior of stellar collapse and explosions. II. Nonlinear evolution, 49, 890 (1994)

View on Pith 1994

[29] [28]

C. O. Lousto and R. H. Price, Head-on collisions of black holes: The particle limit , Phys. Rev. D 55, 2124 (1997)

View on Pith 1997

[30] [29]

K. Martel, Gravitational waveforms from a point particle orbiting a Schwarzschild black hole , Phys. Rev. D 69, 044025 (2004)

View on Pith 2004

[31] [30]

K. Martel and E. Poisson, One-parameter family of time- symmetric initial data for the radial infall of a particle into a Schwarzschild black hole , Phys. Rev. D 66, 084001 (2002)

View on Pith 2002

[32] [31]

C. F. Sopuerta, P. Sun, P. Laguna, and J. Xu, A Toy Model for Testing Finite Element Methods to Simulate Extreme-Mass-Ratio-Binary Systems, gr-qc/0507112

View on Pith Pith review arXiv

[33] [32]

C. Cutler, D. Kenneﬁck, and E. Poisson, Gravita- tional radiation reaction for bound motion around a Schwarzschild black hole , Phys. Rev. D 50, 3816 (1994)

View on Pith 1994

[34] [33]

L. S. Finn and K. S. Thorne, Gravitational waves from a compact star in a circular, inspiral orbit, in the equatoria l plane of a massive, spinning black hole, as observed by LISA, Phys. Rev. D 62, 124021 (2000)

View on Pith 2000

[35] [34]

M. Shibata, Gravitational waves induced by a particle or- biting around a rotating black hole , Prog. Theor. Phys. 90, 595 (1993)

View on Pith 1993

[36] [35]

M. Shibata, Gravitational waves by compact stars orbit- ing around rotating supermassive black holes , Phys. Rev. D 50, 6297 (1994)

View on Pith 1994

[37] [36]

S. A. Hughes, Evolution of circular, nonequatorial orbits of Kerr black holes due to gravitational-wave emission. II. Inspiral trajectories and gravitational waveforms , Phys. Rev. D 64, 064004 (2001)

View on Pith 2001

[38] [37]

E. Poisson, An introduction to the Lorentz-Dirac equa- tion, gr-qc/9912045

View on Pith Pith review arXiv

[39] [38]

P. A. M. Dirac, Classical theory of radiating electrons , Proc. R. Soc. London A167, 148 (1938)

View on Pith 1938

[40] [39]

Y. Mino, M. Sasaki, and T. Tanaka, Gravitational radia- tion reaction to a particle motion , Phys. Rev. D 55, 3457 (1997)

View on Pith 1997

[41] [40]

T. C. Quinn and R. M. Wald, Axiomatic approach to elec- tromagnetic and gravitational radiation reaction of parti - cles in curved spacetime , Phys. Rev. D 56, 3381 (1997)

View on Pith 1997

[42] [41]

E. Poisson, The Motion of Point Particles in Curved Spacetime, Living Rev. Relativity 7, 6 (2004), http://www.livingreviews.org/lrr-2004-6

View on Pith 2004

[43] [42]

A good summary of the current state and recent progress of this ﬁeld can be found in a special issue of the journal Classical and Quantum Gravity: Gravitational radiation from binary black holes: Advances in the perturbative ap- proach, edited by C. O. Lousto; Class. Quantum Grav. 22, number 15 (2005) (Institute of Physics Publishing, Bristol, 2005)

View on Pith 2005

[44] [43]

A. Pound, E. Poisson, and B. G. Nickel, Limitations of the adiabatic approximation to the gravitational self-for ce, Phys. Rev. D 72, 124001 (2005)

View on Pith 2005

[45] [44]

S. Drasco and S. A. Hughes, Rotating black hole orbit functionals in the frequency domain , Phys. Rev. D 69, 044015 (2004)

View on Pith 2004

[46] [45]

W. Schmidt, Celestial mechanics in Kerr spacetime , Class. Quant. Grav. 19, 2743 (2002)

View on Pith 2002

[47] [46]

M. Sasaki and T. Nakamura, Gravitational radiation from a Kerr black hole. I , Prog. Theor. Phys. 67, 1788 (1982)

View on Pith 1982

[48] [47]

D. C. Wilkins, Bound Geodesics in the Kerr Metric , Phys. Rev. D 5, 814 (1972)

View on Pith 1972

[49] [48]

R. H. Boyer and R. W. Lindquist, Maximal Analytic Ex- tension of the Kerr Metric , J. Math. Phys. 8, 265 (1967)

View on Pith 1967

[50] [49]

R. M. Wald, On perturbations of a Kerr black hole , J. Math. Phys. 14, 1453 (1973). 28

View on Pith 1973

[51] [50]

E. Newman and R. Penrose, An approach to Gravita- tional Radiation by a Method of Spin Coeﬃcients , J. Math. Phys. 3, 566 (1962)

View on Pith 1962

[52] [51]

S. Chandrasekhar, The Mathematical Theory of Black Holes (Oxford University Press, New York, 1983)

View on Pith 1983

[53] [52]

E. Poisson, Absorption of mass and angular momentum by a black hole: Time-domain formalisms for gravita- tional perturbations, and the small-hole/slow-motion ap- proximation, Phys. Rev. D 70, 084044 (2004)

View on Pith 2004

[54] [53]

G. Khanna, Teukolsky evolution of particle orbits around Kerr black holes in the time domain: Elliptic and inclined orbits, Phys. Rev. D 69, 024016 (2004)

View on Pith 2004

[55] [54]

R. Fujita and H. Tagoshi, New Numerical Methods to Evaluate Homogeneous Solutions of the Teukolsky Equa- tion, Prog. Theor. Phys. 112, 415 (2004)

View on Pith 2004

[56] [55]

G. Arfken, Mathematical Methods for Physicists (third edition, Academic Press, Orlando, FL, 1985)

View on Pith 1985

[57] [56]

R. A. Breuer, Gravitational Perturbation Theory and Synchrotron Radiation, Lecture Notes in Physics Vol. 44 (Springer-Verlag, Berlin, 1975)

View on Pith 1975

[58] [57]

M. Sasaki and H. Tagoshi, Analytic Black Hole Perturbation Approach to Gravitational Ra- diation, Living Rev. Relativity 6, 6 (2003), http://www.livingreviews.org/lrr-2003-6/

View on Pith 2003

[59] [58]

W. Kinnersly, Type D Vacuum Metrics , J. Math. Phys. 10, 1195 (1969)

View on Pith 1969

[60] [59]

Y. Mino et al., Black hole perturbation , Prog. Theor. Phys. Suppl. 128, 1 (1997)

View on Pith 1997

[61] [60]

R. D. Blandford and K. S. Thorne, Applications of Classical Physics , unpublished book, available at http://www.pma.caltech.edu/Courses/ph136/yr2004/, Chapt. 26

View on Pith

[62] [61]

R. A. Isaacson, Gravitational Radiation in the Limit of High Frequency. II. Nonlinear Terms and the Eﬀective Stress Tensor, Phys. Rev. 166, 1272 (1968)

View on Pith 1968

[63] [62]

S. A. Teukolsky and W. H. Press, Perturbations of Rotat- ing Black Hole. III. Interaction of the Hole with Gravita- tional and Electromagnetic Radiation , Astrophys. J. 193, 443 (1974)

View on Pith 1974

[64] [63]

C. Cutler, private communication

View on Pith

[65] [64]

J. Gair, private communication

View on Pith

[66] [65]

W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical Recipes in C++: The Art of Sci- entiﬁc Computing (Cambridge University Press, Cam- bridge, 2002)

View on Pith 2002

[67] [66]

P. C. Peters and J. Mathews, Gravitational Radiation from Point Masses in a Keplerian Orbit , Phys. Rev. 131, 435 (1963)

View on Pith 1963

[68] [67]

K. S. Thorne, Multipole Expansions of Gravitational Ra- diation, Rev. Mod. Phys. 52, 299 (1980)

View on Pith 1980

[69] [68]

D. Kenneﬁck, Stability under radiation reaction of circu- lar equatorial orbits around Kerr black holes , Phys. Ref. D 58, 064012 (1998)

View on Pith 1998

[70] [69]

M. Shibata and K. Glampedakis, private communica- tions

View on Pith