Using LISA EMRI sources to test off-Kerr deviations in the geometry of massive black holes

Curt Cutler; Leor Barack

REVIEW

Using LISA EMRI sources to test off-Kerr deviations in the geometry of massive black holes

Leor Barack, Curt Cutler

General Relativity and Quantum Cosmology · Submitted 5 Dec 2006 · 32 references

Pith's verdict: A solid, honest forecast: LISA can pin Q/M^3 to 10^-4–10^-2 from bright EMRIs, and this is the number to cite — provided you read it as order-of-magnitude, which the authors themselves say.

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CitationCurt Cutler, Leor Barack. "Using LISA EMRI sources to test off-Kerr deviations in the geometry of massive black holes." arXiv:gr-qc/0612029 (2006). https://pith.science/paper/TNKUE5OY

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Editor's note

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Bottom line: this is the paper to cite for how well LISA can measure a massive black hole's quadrupole moment, and the numbers are believable at the order-of-magnitude level the authors claim for them. It deserves a referee and will get cited. It is not the last word on the Q-coupling, and the authors know that better than anyone reading it quickly will. What is actually new: Ryan (1997) did this for circular, equatorial orbits and no LISA response. Barack and Cutler do generic orbits, a 15-parameter Fisher matrix that includes sky position, spin direction, orbital orientation and the full Doppler plus spacecraft-rotation modulation, and they get ΔQ̃ ~ 10^-4, 10^-3, 10^-2 for M = 10^5.5, 10^6, 10^6.5. At the low-mass end that is roughly two orders tighter than Ryan. What they do well: Eqs. (4)–(8) are written out in full, so you can reimplement the whole thing. Sec. III.C is a real robustness check — strip the (2πMν)^{2/3} terms and ΔQ̃ moves by less than a factor 3. They invert the Fisher matrix two ways (SVD and Gauss-Jordan, agreeing to ~20%) and discuss condition numbers up to 10^22 without flinching. Table II, which shows how much adding Q̃ degrades ΔS̃ (by up to a factor 54), is the kind of result most forecast papers bury. Where it is soft: the Q-coupling. Right after Eq. (8) they say Eq. (7) should carry a Q̃ term but deriving it is nontrivial, so it is dropped; the Q̃ term in Eq. (5) is imported from Gair & Glampedakis Eq. (44), which they note is missing an e² sin²λ piece. The III.C check varies PN order but leaves the Q coefficients untouched, so it does not directly probe ∂h/∂Q̃. Two things bound this: e_LSO ≤ 0.3 with the omitted pieces higher order in e, and dropping the 2/3-PN terms does shift the relative weight of the Q terms, so III.C is a partial probe rather than none. Still, the coefficients are asserted, not derived, and a tens-of-percent error in them would move the quoted numbers. Minor: ν_LSO is fixed at the Schwarzschild circular value for all spins and eccentricities, which they acknowledge. One correction to the reader's report: the sentence record says no limitations are stated. That is wrong — Sec. II.C, Sec. III.C and the Conclusions state several, candidly. Who it is for: LISA parameter-estimation people and anyone writing a no-hair-test proposal. Send it out.

Referee report

Significance

If the forecast holds, every bright EMRI becomes a quantitative, source-by-source test of the no-hair relation Q = -S^2/M, which is a genuinely falsifiable prediction rather than a consistency check. The paper's strengths are concrete and worth naming: the evolution equations (4)-(8) are written out in full so the waveform model can be reproduced and audited; the 15-dimensional parameter set is enumerated explicitly in Eq. (3) and Table I; the Q terms are traced to specific published sources (Lai et al.; Gair and Glampedakis) rather than asserted; and the numerical inversion is checked two independent ways (singular-value decomposition versus Gauss-Jordan in Fig. 3) with an explicit reconditioning argument. The authors also state their model's limitations in the text rather than burying them, and the 'dumbed-down' comparison in Sec. III.C is a real, if partial, robustness test. The claimed factor-of-a-few calibration is appropriate to the evidence presented.

Major objections (2)

[§II.C, Eqs. (5)-(8)] The headline number is ∆Q̃ = [(Γ^-1)_Q̃Q̃]^1/2, so it depends directly on the fidelity of ∂h/∂Q̃, and that derivative is generated entirely by the three Q̃ terms added to Eqs. (5), (6) and (8). The authors state immediately after Eq. (8) that Eq. (7) 'should also contain a term ∝ Q̃' but that deriving it 'would be nontrivial', so it is dropped; and the Q̃ term in Eq. (5) is imported from Eq. (44) of Gair and Glampedakis, which the authors themselves note is missing a piece proportional to e^2 sin^2(lambda). The robustness check in Sec. III.C removes the (2πMν)^{2/3} terms but leaves the Q̃ coefficients themselves untouched, so it probes the PN order content of the model, not the accuracy of the Q-coupling. I want to be clear that I do not regard this as undermining the paper: the omission is bounded by e_LSO ≤ 0.3 and e^2 ≲ 0.1, and the claim is explicitly order-of-magnitude. But the caveat would be much stronger as evidence than as assertion, and the test is cheap. I recommend a short addition in which the coefficients multiplying Q̃ in Eqs. (5), (6) and (8) are rescaled by, say, ±30% and ±50%, and the resulting shift in ∆Q̃ is reported for one or two representative points in Fig. 2. If ∆Q̃ moves by less than the factor of ~3 the authors already claim, the caveat is converted into a demonstrated robustness result; if it moves more, readers deserve to know before the 10^-4-10^-2 range is quoted elsewhere.
[§III.A, Eq. (24), Fig. 1] The representative angles in Eq. (24) were selected precisely because they reproduce the median ∆Q̃ for each mass, and are then held fixed while (µ, S, e_LSO) are surveyed. That is a defensible strategy for an order-of-magnitude exploration, and the 108-point scan behind Fig. 1 is the right way to calibrate it. The issue is how the result is framed rather than how it was computed: the abstract states that the results 'depend only weakly on the eccentricity of the orbit or the BH's spin' but says nothing about the orientation dependence, even though orientation is the largest of the three variations, with log10 standard deviations of 0.13-0.17 in Fig. 1 and a stated spread of up to a factor 4 in Sec. IV. A reader who takes the abstract numbers as generic could be misled by up to a factor 4 in either direction. I ask that the abstract and the first paragraph of Sec. IV state explicitly that the quoted values are medians over source and spin orientation, with a spread of roughly a factor 1.5 (one sigma) and up to a factor 4 across the sampled orientations. This is a one-sentence change and it makes the claim more accurate, not weaker.

Minor objections (7)

[§III.A] The text and Fig. 1 caption refer to '108 different values' of (θ_S, φ_S, θ_K, φ_K, λ), but the grid as printed appears to list three values for each of the five angles, which would give 243 combinations. Please reconcile the stated number of grid points with the enumerated values, since the median and standard deviation in Fig. 1 depend on which points were actually sampled.
[Table II] The distinction between the bold-face and plain-face entries carries the entire comparison between the 15-parameter and 14-parameter fits, and it will not survive black-and-white printing or plain-text extraction. Please use separate columns, or add an explicit marker in a dedicated column, so the two sets of numbers remain distinguishable in any format.
[Eq. (11)] The LSO frequency is fixed at the Schwarzschild circular value for all spins and all eccentricities considered, which the authors acknowledge as a simplification. Since the number of observable cycles is one of the quantities that drives ∆Q̃, it would help to state, even roughly, how much ∆Q̃ would move if ν_LSO were instead taken from the correct Kerr value at the relevant spin, or to add this to the list of caveats in Sec. IV alongside the waveform-systematics caveat.
[Fig. 2, left panel] The caption notes that a few data points were discarded because the initial eccentricity exceeds 0.7, but the figure does not show which points are missing. Please mark the discarded points explicitly or state in the caption how many points are absent for each mass, so a reader can tell whether the visible trend at low mass and high e_LSO is complete.
[§II.B, footnote [30]] The argument that the compact object's spin can be neglected, because it modifies the phase by at most a few radians out of ~10^6 while an excess quadrupole of twice the Kerr value would modify it by ~10^3 radians, is exactly the kind of quantitative justification that belongs in the main text. Consider promoting a one-line version of it into Sec. II.B, since it is what licenses dropping three of the seventeen parameters.
[§IV] The caveat that an off-Kerr best-fit Q could reflect an unclean two-body system rather than a non-Kerr central object is well taken. It may be worth adding that a non-Kerr central object would generally not share the Kerr LSO, so the parameterization through e_LSO and the fixed ν_LSO of Eq. (11) implicitly assumes a Kerr-like plunge even when Q̃ is allowed to vary; this is a second, distinct way in which the test is not fully model-independent.
[Acknowledgments and abstract] There are small typographical errors to fix: 'We thank for Kip Thorne for encouraging us' in the Acknowledgments, and the capitalized 'Inspiral' in the abstract phrase 'the full parameter space of Inspiral sources'.

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The paper

The paper claims

The paper asks whether LISA can measure the quadrupole moment of a massive black hole well enough to check that the spacetime really is a Kerr black hole, and answers with a forecast of a few parts in ten thousand to a few parts in a 100, 1

The reading

General relativity says a black hole is fully described by two numbers, its mass $M$ and its spin $S$; every higher multipole moment is then fixed, and in particular the mass quadrupole is $Q = -S^2/M$. This paper asks a concrete observational question: when LISA watches a small stellar-mass body spiral into a million-solar-mass object, can the waveform be used to measure $Q$ as if it were a free parameter, and thereby check whether the measured value agrees with the Kerr formula? The authors extend their earlier approximate inspiral waveform family so that $Q$ enters the orbital evolution as an independent quantity, then compute the Fisher information matrix over a fifteen-parameter source description and invert it to get the expected measurement error. For one year of data at signal-to-noise ratio 100 they find $Q/M^3$ measurable to about $10^{-4}$, $10^{-3}$ or $10^{-2}$ for central masses of $10^{5.5}$, $10^6$ and $10^{6.5}$ solar masses, with only mild dependence on orbital eccentricity or spin. The point of the exercise is that each bright inspiral would then supply its own quantitative null test of the Kerr relation, in the same spirit as the classic binary-pulsar tests of general relativity.

What carries the argument

The argument is carried by two pieces of machinery working together. The first is the authors' 'analytic kludge' waveform family: the inspiralling pair is treated at any instant as a Newtonian binary emitting a quadrupole-form waveform, while post-Newtonian equations secularly evolve the orbital frequency, eccentricity, pericenter precession angle and Lense-Thirring precession angle, and the LISA response is built from time-dependent transfer functions including the Doppler delay from the constellation's motion about the Sun. To this the authors add three lowest-order terms proportional to $Q$: a Newtonian-like contribution to the pericenter precession rate and to the precession of the orbital plane, both taken from published treatments of oblate bodies, and a contribution to the frequency evolution obtained by combining the Newtonian energy-frequency relation with an adopted energy-loss formula. The second piece is the Fisher information matrix over the resulting fifteen parameters, including $Q/M^3$, inverted to give the variance-covariance matrix and hence the expected error in $Q$. The whole estimate rests on the assumption that this kludge's sensitivity to $Q$ tracks the sensitivity of the true general-relativistic waveform.

Extended reading notes

Core claim

The central claim is a forecast rather than a detection: for the brightest expected extreme-mass-ratio inspirals, LISA should determine the dimensionless quadrupole moment $Q/M^3$ of the central massive object to roughly $10^{-4}$ at $10^{5.5}$ solar masses, $10^{-3}$ at $10^6$ solar masses, and $10^{-2}$ at $10^{6.5}$ solar masses, assuming one year of coherent data and a total signal-to-noise ratio of 100. Because $Q$ is treated as independent of $M$ and $S$, a measured value that departs from $-S^2/M$ would signal a spacetime that is not Kerr. The authors present this as an improvement on the earlier estimate by Ryan, which assumed circular equatorial orbits and ignored the modulations caused by LISA's own motion; here the orbits are generic and the spacecraft Doppler and constellation-rotation modulations are included. They also report that the accuracy depends only weakly on eccentricity and spin, and that the price of adding $Q$ to the parameter set is a degradation of the other parameters, most severely of the spin magnitude, whose measurement error grows by factors of up to roughly fifty because the $Q$ and $S$ terms in the evolution equations scale with frequency in nearly the same way.

Load-bearing premise

The forecast assumes that the way this approximate waveform responds to a change in the quadrupole moment is close enough to the way a true general-relativistic waveform would respond, even though the quadrupole enters only through three lowest-order terms, the correction to the eccentricity evolution is omitted outright, and the frequency-evolution term is taken from a published formula the authors themselves note is missing a piece proportional to $e^2$.

Editorial extensions

If this is right

Each sufficiently bright EMRI becomes a standalone null test of the no-hair relation $Q = -S^2/M$, with the measured quadrupole compared against the value the measured mass and spin predict.
The test is most powerful for the lowest-mass central objects considered: the forecast error grows by about two orders of magnitude between $10^{5.5}$ and $10^{6.5}$ solar masses at fixed signal-to-noise ratio.
Because the error scales roughly inversely with signal-to-noise ratio, even marginally detectable sources at signal-to-noise 30 to 35 would still constrain $Q/M^3$ to within a factor of a few of the quoted numbers.
Adding $Q$ to the search parameter set measurably worsens the recovery of the other source parameters, especially the spin magnitude, so any claim of a quadrupole measurement comes bundled with a weaker spin measurement.
A measured quadrupole away from the Kerr value in a single source could reflect an unclean two-body environment, such as an accretion disk or a third body, rather than a genuine departure from Kerr geometry.

Reading between the lines

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

The forecast is a statement about statistical error only; a systematic error in the theoretical waveform template of comparable size would dominate the budget at the low-mass end, so the realistic ceiling on this test is set by waveform modelling rather than by LISA's sensitivity.
Because the quadrupole and spin terms enter the precession rates with nearly the same frequency scaling, the strong correlation the authors report suggests that a reparameterisation in which spin and quadrupole are measured jointly, rather than one at a time, would report the result more honestly.
The same Fisher-matrix machinery could be run with the leading multipoles above the quadrupole promoted to free parameters, which is the natural next step and was done in simplified form by the earlier work this paper extends.
If the kludge's $Q$ dependence is the weakest link, a useful cross-check is to repeat the forecast with a numerically generated inspiral in a weakly deformed Kerr spacetime, where the trajectory's dependence on the deformation is computed rather than modelled.

Original abstract

Inspirals of stellar-mass compact objects into $\sim 10^6 M_{\odot}$ black holes are especially interesting sources of gravitational waves for LISA. We investigate whether the emitted waveforms can be used to strongly constrain the geometry of the central massive object, and in essence check that it corresponds to a Kerr black hole (BH). For a Kerr BH, all multipole moments of the spacetime have a simple, unique relation to $M$ and $S$, the BH's mass and spin; in particular, the spacetime's mass quadrupole moment is given by $Q=- S^2/M$. Here we treat $Q$ as an additional parameter, independent of $M$ and $S$, and ask how well observation can constrain its difference from the Kerr value. This was already estimated by Ryan, but for simplified (circular, equatorial) orbits, and neglecting signal modulations due to the motion of the LISA satellites. Here we consider generic orbits and include these modulations. We use a family of approximate (post-Newtonian) waveforms, which represent the full parameter space of Inspiral sources, and exhibit the main qualitative features of true, general relativistic waveforms. We extend this parameter space to include (in an approximate manner) an arbitrary value of $Q$, and construct the Fisher information matrix for the extended parameter space. By inverting the Fisher matrix we estimate how accurately $Q$ could be extracted from LISA observations. For 1 year of coherent data from the inspiral of a $10 M_{\odot}$ BH into rotating BHs of masses $10^{5.5} M_{\odot}$, $10^6 M_{\odot}$, or $10^{6.5} M_{\odot}$, we find $\Delta (Q/M^3) \sim 10^{-4}$, $10^{-3}$, or $10^{-2}$, respectively (assuming total signal-to-noise ratio of 100, typical of the brightest detectable EMRIs). These results depend only weakly on the eccentricity of the orbit or the BH's spin.

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, 8,629 input tokens, $0.0004 reported.

What the abstract itself states, as probabilities: claims first 0.05 · states limitation 0.82 · human participants 0.01 · controlled comparison 0.16 · randomized assignment 0.01 · states quantitative result 0.99 · compares with prior results 0.95 · mentions code or data availability 0.02.

The abstract, sentence by sentence

arXiv listing abstract v1. Results and the main claim are underlined; show every role.

Inspirals of stellar-mass compact objects into $\sim 10^6 M_{\odot}$ black holes are especially interesting sources of gravitational waves for LISA. We investigate whether the emitted waveforms can be used to strongly constrain the geometry of the central massive object, and in essence check that it corresponds to a Kerr black hole (BH). For a Kerr BH, all multipole moments of the spacetime have a simple, unique relation to $M$ and $S$, the BH's mass and spin; in particular, the spacetime's mass quadrupole moment is given by $Q=- S^2/M$. Here we treat $Q$ as an additional parameter, independent of $M$ and $S$, and ask how well observation can constrain its difference from the Kerr value. This was already estimated by Ryan, but for simplified (circular, equatorial) orbits, and neglecting signal modulations due to the motion of the LISA satellites. Here we consider generic orbits and include these modulations. We use a family of approximate (post-Newtonian) waveforms, which represent the full parameter space of Inspiral sources, and exhibit the main qualitative features of true, general relativistic waveforms. We extend this parameter space to include (in an approximate manner) an arbitrary value of $Q$, and construct the Fisher information matrix for the extended parameter space. By inverting the Fisher matrix we estimate how accurately $Q$ could be extracted from LISA observations. For 1 year of coherent data from the inspiral of a $10 M_{\odot}$ BH into rotating BHs of masses $10^{5.5} M_{\odot}$, $10^6 M_{\odot}$, or $10^{6.5} M_{\odot}$, we find $\Delta (Q/M^3) \sim 10^{-4}$, $10^{-3}$, or $10^{-2}$, respectively (assuming total signal-to-noise ratio of 100, typical of the brightest detectable EMRIs). These results depend only weakly on the eccentricity of the orbit or the BH's spin.

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	Inspirals of stellar-mass compact objects into $\sim 10^6 M_{\odot}$ black holes are especially interesting sources of gravitational waves for LISA.	background 1.00	0.06	0.02	asserted 0.94
s1	We investigate whether the emitted waveforms can be used to strongly constrain the geometry of the central massive object, and in essence check that it corresponds to a Kerr black hole (BH).	contribution 0.90	0.50	0.06	hedged possibility 0.64
s2	For a Kerr BH, all multipole moments of the spacetime have a simple, unique relation to $M$ and $S$, the BH's mass and spin; in particular, the spacetime's mass quadrupole moment is given by $Q=- S^2/M$.	background 1.00	0.05	0.03	asserted 1.00
s3	Here we treat $Q$ as an additional parameter, independent of $M$ and $S$, and ask how well observation can constrain its difference from the Kerr value.	contribution 0.64	0.70	0.04	asserted 0.63
s4	This was already estimated by Ryan, but for simplified (circular, equatorial) orbits, and neglecting signal modulations due to the motion of the LISA satellites.	background 0.65	0.03	0.02	asserted 1.00
s5	Here we consider generic orbits and include these modulations.	contribution 0.85	0.90	0.02	asserted 0.99
s6	We use a family of approximate (post-Newtonian) waveforms, which represent the full parameter space of Inspiral sources, and exhibit the main qualitative features of true, general relativistic waveforms.	method 0.98	0.77	0.02	asserted 1.00
s7	We extend this parameter space to include (in an approximate manner) an arbitrary value of $Q$, and construct the Fisher information matrix for the extended parameter space.	method 0.94	0.95	0.03	asserted 0.99
s8	By inverting the Fisher matrix we estimate how accurately $Q$ could be extracted from LISA observations.	method 0.95	0.94	0.05	asserted 0.74
s9	For 1 year of coherent data from the inspiral of a $10 M_{\odot}$ BH into rotating BHs of masses $10^{5.5} M_{\odot}$, $10^6 M_{\odot}$, or $10^{6.5} M_{\odot}$, we find $\Delta (Q/M^3) \sim 10^{-4}$, $10^{-3}$, or $10^{-2}$, respectively (assuming total signal-to-noise ratio of 100, typical of the brightest detectable EMRIs).	result 1.00	0.96	0.85	asserted 1.00
s10	These results depend only weakly on the eccentricity of the orbit or the BH's spin.	result 0.71	0.90	0.12	asserted 0.99

What kind of paper the classifier reports this is: theoretical result 0.67 · evidence from simulation or computation 0.82.

What was examined, and what was not

sources read

arXiv listing abstract v1

not examined

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

levels run

P abstract

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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 3.** FIG. 3: Comparison of the values of ∆

Showing 3 of the paper's 4 figures. See all figures in the PDF ↗ Figures reproduced from arXiv:gr-qc/0612029 by the authors.

References

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The significance of first post-adiabatic contributions for scalar charge measurements with intermediate and extreme mass ratio inspirals
gr-qc 2026-07 accept novelty 6.5 of 10

Neglecting 1PA gravitational self-force biases intrinsic EMRI parameters while scalar-charge inference remains robust; pure-GR templates produce large biases and underestimated errors on charged signals.
Probing parity-breaking black-hole geometry with extreme-mass-ratio inspirals
gr-qc 2026-10 accept novelty 6.0 of 10

For a one-year inspiral into a rapidly rotating black hole, the waveform mismatch reaches a detectable level at epsilon approximately 10^{-3}.
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...
Beyond circular and equatorial orbits: Bayesian constraint on vector charge with the adiabatic inspirals of generic Kerr geodesics
gr-qc 2026-09 conditional novelty 6.0 of 10

A new mode-sum formula gives the electromagnetic Carter-constant flux for generic nonresonant Kerr orbits, enabling Bayesian estimation of the vector charge of an EMRI secondary.
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.
Extreme mass-ratio inspiral within an ultralight scalar cloud I. Scalar radiation
gr-qc 2025-07 conditional novelty 6.0 of 10

Scalar radiation from an EMRI in an ultralight scalar cloud is computed semi-analytically, showing dipole clouds decelerate and quadrupole clouds accelerate the inspiral, with up to about 100 rad dephasing after 18 months.
An interstellar mission to test astrophysical black holes
gr-qc 2025-04 conditional novelty 6.0 of 10

A concept study suggesting that nanocraft probes could reach the closest black hole in 60 to 75 years and test General Relativity's predictions for the Kerr metric, event horizon, and fundamental constants.
Probing time-dependent scalar wigs with extreme mass ratio inspirals
gr-qc 2024-12 conditional novelty 6.0 of 10

For EMRIs where the smaller black hole carries an oscillating scalar cloud with mass 0.001 <= mu_s m_p <= 0.02, the scalar energy flux is negligible, so the inspiral and gravitational waveform are essentially unchanged.
Leading Higher Derivative Corrections to Multipole Moments of Kerr-Newman Black Hole
hep-th 2024-11 conditional novelty 6.0 of 10

The 4-derivative corrections to Kerr-Newman multipole moments depend only on field-redefinition-invariant couplings, and parity-odd terms turn on multipole moments that vanish in Einstein-Maxwell theory.
Extreme mass-ratio inspirals around a spinning horizonless compact object
gr-qc 2021-06 accept novelty 6.0 of 10

Consistent Teukolsky modeling of EMRIs around spinning horizonless objects shows resonant flux enhancements and projects LISA sensitivity to reflectivity at the 10^-8 level.
Gravitational Footprints of Black Holes and Their Microstate Geometries
hep-th 2021-04 conditional novelty 6.0 of 10

Almost-BPS extremal black holes have multipoles that depend on a charge-to-mass dial h and differ from Kerr, and their horizonless microstate geometries reproduce those multipoles up to small, sign-random corrections ...
Distinguishing fuzzballs from black holes through their multipolar structure
hep-th 2020-07 conditional novelty 6.0 of 10

A general method for extracting multipole moments of stationary spacetimes shows that four-dimensional fuzzball microstates have multipole moments typically larger than Kerr black holes of the same mass and spin.
Detecting scalar fields with Extreme Mass Ratio Inspirals
gr-qc 2020-04 conditional novelty 6.0 of 10

A small body's scalar charge produces extra radiation during an extreme mass ratio inspiral, dephasing the gravitational wave signal by amounts LISA could detect.
Love in Extrema Ratio
gr-qc 2019-05 conditional novelty 6.0 of 10

In an extreme-mass-ratio inspiral, the tidal Love number of the massive central object enters the gravitational-wave phase at leading order in the mass ratio, making EMRIs a sensitive probe of the central object's tid...
Science with the space-based interferometer LISA. V: Extreme mass-ratio inspirals
gr-qc 2017-03 accept novelty 6.0 of 10

Across twelve astrophysical models, LISA should detect between roughly one and a few thousand extreme mass-ratio inspirals per year, with masses and spins measurable to parts in 10^4 to 10^6.
Slowly Rotating Black Holes in Dynamical Chern-Simons Gravity: Deformation Quadratic in the Spin
gr-qc 2012-06 accept novelty 6.0 of 10

A stationary, axisymmetric black hole metric in dynamical Chern-Simons gravity is derived to quadratic order in spin, revealing a Petrov type I classification and no exact Carter-like constant.
Towards a generic test of the strong field dynamics of general relativity using compact binary coalescence
gr-qc 2011-10 conditional novelty 6.0 of 10

A Bayesian odds-ratio framework that tests each subset of post-Newtonian phase coefficients separately, then combines them, can detect generic deviations from General Relativity in simulated Advanced LIGO/Virgo binary...
Probing near-zone magnetic fields with extreme mass-ratio inspirals
gr-qc 2026-07 conditional novelty 5.0 of 10

A magnetized Schwarzschild background shifts EMRI orbital dynamics and GW waveforms, with B~10^9 G producing ~1.3 rad dephasing over one year for a 10^6 M_sun system.
Wet Extreme Mass Ratio Inspirals May Be More Common For Spaceborne Gravitational Wave Detection
astro-ph.HE 2021-04 conditional novelty 5.0 of 10

Wet EMRIs, formed when an AGN accretion disk captures and migrates stellar-mass black holes inward, may outnumber dry loss-cone EMRIs among LISA detections by one to two orders of magnitude.
Tests of General Relativity with Binary Black Holes from the second LIGO-Virgo Gravitational-Wave Transient Catalog
gr-qc 2020-10 accept novelty 5.0 of 10

No evidence for deviations from general relativity is found in LIGO-Virgo binary black hole events, with improved constraints on waveform parameters, graviton mass, and ringdown properties.
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.
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...
Testing Black Holes with Interstellar Missions: I. Orbiting Probes
gr-qc 2026-05 unverdicted novelty 4.0 of 10

Preliminary analysis of orbiting spacecraft around a black hole to test the compact object's nature and General Relativity under the assumption of deceleration capability.
Measuring the Kerr spin parameter of regular black holes from their shadow
gr-qc 2013-09 conditional novelty 4.0 of 10

For non-rotating or slowly rotating regular black holes the shadow, iron line, and ISCO methods yield different inferred Kerr spins, so combining them can test the Kerr hypothesis; for near-extremal objects all three ...
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.
Black Hole Based Tests of General Relativity
gr-qc 2016-02 accept novelty 3.0 of 10

A structured survey of black-hole-based tests of general relativity, covering model-independent parameterizations and four specific alternative theories, with current and projected constraints from gravitational and e...
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 ...
Waveform Modelling for the Laser Interferometer Space Antenna
gr-qc 2023-11 unverdicted novelty 2.0 of 10

A review of existing waveform models for LISA sources and the challenges that must still be overcome.
New Horizons for Fundamental Physics with LISA
gr-qc 2022-05 accept novelty 2.0 of 10

The LISA Fundamental Physics Working Group catalogues the open questions in strong-gravity, black-hole, dark-matter and dark-energy physics that LISA could address, and lists the modelling work needed to get there.
Testing the nature of dark compact objects with gravitational waves
gr-qc 2021-05 accept novelty 2.0 of 10

Gravitational-wave observations can distinguish black holes from horizonless exotic compact objects through multipole moments, tidal deformability, ringdown spectra, and post-merger echoes, and current data remain con...
Prospects for Fundamental Physics with LISA
gr-qc 2020-01 unverdicted novelty 2.0 of 10

The LISA fundamental-physics working group maps six gravitational-wave source classes onto the beyond-standard-model physics each could probe, without quantitative forecasts.
The unique potential of extreme mass-ratio inspirals for gravitational-wave astronomy
astro-ph.HE 2019-03 conditional novelty 2.0 of 10

Extreme mass-ratio inspirals will let LISA measure black hole masses, spins, distances and spacetime multipoles with percent-to-parts-per-million precision, provided waveform models reach second-order self-force accuracy.
Testing the black hole "no-hair" hypothesis
gr-qc 2016-07 conditional novelty 2.0 of 10

The Kerr no-hair hypothesis is a testable null hypothesis, and ringdown, stellar-orbit, accretion-disk and shadow observations can check it at signal-to-noise ratios the review quantifies.
Gravitational Wave Tests of General Relativity with Ground-Based Detectors and Pulsar Timing Arrays
gr-qc 2013-04 conditional novelty 2.0 of 10

Gravitational wave observations of compact binary mergers and pulsar timing can constrain alternatives to general relativity in the strong-field, dynamical regime, and the review catalogues the projected bound for eac...
Physics, Astrophysics and Cosmology with Gravitational Waves
gr-qc 2009-03 accept novelty 2.0 of 10

The paper reviews the physics, sources, detectors, data analysis and scientific payoff of gravitational wave astronomy, forecasting that upgraded ground-based interferometers should reach regular detections around 2014.
Intermediate and Extreme Mass-Ratio Inspirals -- Astrophysics, Science Applications and Detection using LISA
astro-ph 2007-03 accept novelty 2.0 of 10

Extreme and intermediate mass-ratio inspirals are argued to be uniquely valuable LISA sources for measuring black-hole masses and spins and for testing general relativity in strong gravity.

How the literature uses it

112 arXiv papers cite this in 193 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 · 149 sentences without a confident label

Contests it 1 paper

However, in any case, this term from [ref] is only accurate to $O(λ^0)$ (as also mentioned in [ref] ), and moreover mixes contributions from $M_2$ and $-S_1^2/M$ as these are indistinguishable in Kerr.

On Detecting Equatorial Symmetry Breaking with LISA · Overview and discussion · contest 0.72

Builds on it 3 papers

The “analytic kludge” formalism for EMRIs, pioneered by Barack and Cutler [ref] , and expanded here by us to include effects of odd parity multipoles $S_2,M_3$ that break equatorial symmetry, was introduced in the previous Section.

On Detecting Equatorial Symmetry Breaking with LISA · Measuring Equatorial Symmetry Breaking with LISA · 0.85
Fransen and Mayerson [ref] went beyond the Barack-Cutler work [ref] by including, for the first time, a current quadrupole and a mass octupole moments as independent parameters.

Probing Kerr symmetry breaking with LISA extreme-mass-ratio inspirals · Introduction · 0.92
This description extends other model independent parameterizations via multipole moments [ref] , tidal deformabilities (Love numbers) [ref] , and quasinormal modes [ref] .

Gravitational wave signatures of departures from classical black hole scattering · Introduction · 0.83

Uses its method or tool 5 papers

We will use the “analytic kludge” formalism developed by Barack and Cutler [ref] to investigate the accuracy that LISA can measure the equatorial symmetry-breaking dimensionless multipoles $S_2/M^3$ and $M_3/M^4$ for EMRIs.

On Detecting Equatorial Symmetry Breaking with LISA · Introduction · 1.00
In this work, we choose to use the AK method, which is also used in the previous analysis for LISA [ref] and TianQin [ref] .

Science with the TianQin Observatory: Preliminary Results on Testing the No-hair Theorem with EMRI · Contribution of quadrupole moment to EMRI waveforms · 0.98
Our choice for the waveform generator relies on the popular Analytic Kludge (AK) model for the generation of inspiraling EMRI waveforms [ref] .

EMRI_MC: A GPU-based Python code for Bayesian inference of EMRI waveforms · Statement of need · 0.99

Uses its data or values 3 papers

The analytic kludge waveforms were used by Barack and Cutler to estimate that LISA could measure the masses of both EMRI bodies as well as the massive BH spin to fractional accuracy $∼10^-5-10^-4$ [ref] , and the quadrupole $M_2$ to within $∼10^-4-10^-2$ [ref] .

On Detecting Equatorial Symmetry Breaking with LISA · Generic Orbits: The Analytic Kludge · 0.90
As a historical benchmark, the Barack–Cutler Fisher analysis for one year of LISA data at signal-to-noise ratio 100 found indicative uncertainties $Δ(Q/M^3)∼10^-4,10^-3,10^-2$ for central masses $10^5.5,10^6,10^6.5M_⊙$, respectively [ref] .

G(2) Glueball Boson Stars as Restricted Kerr Mimickers in the Thomas--Fermi Limit · Quantitative multipole discriminant for gravitational-wave observations · 0.85
Nonetheless, for an EMRI with masses $10 M_⊙, 10^6 M_⊙$ and with SNR $∼100$ it is estimated that we will be able to measure the quadrupole moment of the central object with a precision of $∼10^-3$ [ref] , while simultaneously measuring the mass and spin of the black hole to $∼10^-4$.

Fundamental physics and cosmology with LISA · Mapping spacetime around compact massive objects in galactic nuclei · 0.81

Compares with it 4 papers

On the other hand, the spin and quadrupole contributions in our model appear to differ from those used in Barack and Cutler [ref] as well as those in Fransen and Mayerson [ref] .

Probing Kerr symmetry breaking with LISA extreme-mass-ratio inspirals · Secular Evolution Equations for the Orbital Dynamics · 0.97
We explicitly checked that our differing evolution equations do not change any of the conclusions or main quantitative estimates of [ref] .

On Detecting Equatorial Symmetry Breaking with LISA · Evolution equations · 0.81
In particular, our dephasing is compatible with the results of Refs. [ref] that used “kludge” waveforms, and it agrees within a factor $≈2$, with the results of Ref. [ref] , which used effective-one-body waveforms to model the EMRI signal.

Extreme mass ratio inspirals with spinning secondary: a detailed study of equatorial circular motion · Spin corrections to fluxes and GW phase · 1.00

Cites it as support 1 paper

Measuring this moment thus allows the consistency of the Kerr solution to be checked.[For this test, all factors of the source redshift cancel, so there is no additional uncertainty from the distance measurement as there is for the source masses.] EMRI observations enable this to be done with high precision [ref] .

The unique potential of extreme mass-ratio inspirals for gravitational-wave astronomy · Mapping black hole spacetimes · 0.97

Cites it as background 17 papers

Until recently attention was strongly focused on EMRIs potential to probe the spacetime around, and hence the properties of, the primary black hole [ref] .

Measuring scalar charge with compact binaries: High accuracy modelling with self-force · Introduction · 0.99
In the LISA sensitivity range, such signals can originate e.g. from white dwarf (WD) binaries, intermediate-mass black hole (IMBH) binaries or extreme mass ratio binaries [ref] .

The dark timbre of gravitational waves · Introduction · 0.80
Space-based LISA-like detectors are expected to observe EMRIs over many orbital cycles before the final plunge [ref] .

Inspirals into bosonic dark matter stars and chirp mimickers · Inspiral evolution and chirp mimickers · 0.91

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.

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