pith. sign in

arxiv: 2510.17954 · v2 · submitted 2025-10-20 · 🌀 gr-qc · hep-th

Green function of the P\"{o}schl-Teller potential

Adrien Kuntz This is my paper

Pith reviewed 2026-05-18 05:49 UTC · model grok-4.3

classification 🌀 gr-qc hep-th
keywords Green functionPöschl-Teller potentialRegge-Wheeler-Zerilliblack hole perturbationstime domaincausalityredshift modes
0
0 comments X

The pith

The Pöschl-Teller approximation to the Regge-Wheeler-Zerilli potential permits an exact causal Green function that includes a new early-time piece with exponentially growing modes.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper replaces the Regge-Wheeler-Zerilli potential with the exactly solvable Pöschl-Teller form to derive the full time-domain Green function for black-hole perturbations while enforcing every causality condition. This calculation isolates an additional early-time contribution absent from conventional treatments, which supplies new exponentially growing modes just before the perturbation reaches the potential maximum. The resulting waveform is expressed as the sum of an instantaneous term that propagates strictly on the light cones and a historical term that accumulates the system's entire past trajectory inside those cones. The same Green function is shown to remain regular at redshift-mode frequencies, displaying neither zeros nor poles.

Core claim

Using an approximation of the Regge-Wheeler-Zerilli potential known as the Pöschl-Teller potential, we exactly compute the time-domain Green function of black-hole perturbations while taking into account all causality conditions. We find the existence of an additional early-times piece in the Green function that contributes new exponentially growing modes just before the signal interacts with the maximum of the potential. The waveform itself is decomposed as an instantaneous piece traveling exactly on the light cones of the Green function and a historical piece depending on the past trajectory of the system inside the light cone. We also study redshift modes and show that the Green function,

What carries the argument

Exact time-domain Green function for the Pöschl-Teller potential, fully incorporating causality and decomposed into instantaneous light-cone and historical interior pieces.

If this is right

  • The Green function acquires an early-time piece that standard calculations omit.
  • This piece produces exponentially growing modes prior to the signal reaching the potential peak.
  • Any waveform splits cleanly into a light-cone instantaneous contribution and a history-dependent interior contribution.
  • The Green function remains regular at redshift-mode frequencies and contains neither zeros nor poles.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • If the model approximation is reliable, comparable early-time structures could appear in direct numerical integrations of the full Regge-Wheeler-Zerilli equation.
  • The instantaneous-plus-historical split offers a concrete route to separate prompt and memory effects in black-hole ringdown waveforms.
  • The same exact-solution technique might be applied to other solvable potentials to map out how causal structure changes across different barrier shapes.

Load-bearing premise

The Pöschl-Teller potential approximates the Regge-Wheeler-Zerilli potential closely enough that its exact Green function still captures the essential causal structure and modal content of the true black-hole perturbation problem.

What would settle it

A numerical computation of the Green function for the exact Regge-Wheeler-Zerilli potential that exhibits no early-time exponentially growing modes would show that the Pöschl-Teller model fails to preserve the relevant causal features.

Figures

Figures reproduced from arXiv: 2510.17954 by Adrien Kuntz.

Figure 1
Figure 1. Figure 1: Comparison of the Zerilli potential VZ for ℓ = 2 and the P¨oschl-Teller potential VPT as a function of the tortoise coordinate x. Physically, it can be identified with the signal that reaches an observer at time t at position x for a small localized perturbation emitted at t = 0 at position ¯x. Using the solution for ψ˜ in Eq. (8) with the definition of the source in Eq. (4), it is easy to show that the ti… view at source ↗
Figure 2
Figure 2. Figure 2: Closing the integration contour according to causality conditions. For t < x − x¯, the contour can be closed in the upper half-plane and the Green function is zero. For t > x + |x¯| the contour can be closed in the lower half-plane and picks up the residues at QNM frequencies. Finally, for x − x < t < x ¯ + ¯x (this only exists provided ¯x > 0), the Green function is decomposed as a sum of two contours in … view at source ↗
Figure 3
Figure 3. Figure 3: Comparison of the analytical Green function (26) (shifted to ensure that the maximum of the potential is at x = xm) and the numerical results for an observer situated at x = 100. The upper panel shows the results for an initial perturbation at x¯ = ¯xISCO ≃ 3.69 at the ISCO, while the lower panel has ¯x = 40. The continuous lines show the analytical results with an increas￾ing number of terms N in the sums… view at source ↗
Figure 4
Figure 4. Figure 4: Real part of the wavefunction ψ for a radial infall and a plunge trajectory. We plot each component of the waveform in Eqs. (34,31) separately, where ψQNM refers to the first line of Eq. (31) and ψE to the second line of Eq. (31). We also plot the sum of these three waveforms and the numerical solution to the Zerilli equation using the same trajectory and the code described in Section III C. N = 20 means t… view at source ↗
read the original abstract

We use an approximation of the Regge-Wheeler-Zerilli potential, known as P\"{o}schl-Teller, to exactly compute the time-domain Green function of black hole perturbations in this simplified model, taking into account all causality conditions. We find the existence of an additional early times piece in the Green function, contributing to new exponentially growing modes just before the signal interacts with the maximum of the potential. The waveform itself is decomposed as an instantaneous piece traveling exactly on the light-cones of the Green function and a historical piece depending on the past trajectory of the system inside the light-cone. We also study redshift modes and show that the Regge-Wheeler-Zerilli Green function is regular at their frequency, with no zero nor pole.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 2 minor

Summary. The manuscript approximates the Regge-Wheeler-Zerilli potential by the Pöschl-Teller potential and computes its time-domain Green function exactly while enforcing all causality conditions. It reports an additional early-time contribution to the Green function that produces new exponentially growing modes immediately before the signal reaches the potential maximum. The waveform is decomposed into an instantaneous piece propagating exactly on the light cones and a historical piece depending on the interior of the light cone; the Green function is further shown to be regular at redshift-mode frequencies, possessing neither zeros nor poles.

Significance. If the approximation faithfully captures early-time causal structure, the result would identify previously unrecognized growing-mode content in black-hole perturbation Green functions, with direct implications for the decomposition of ringdown waveforms beyond standard quasinormal-mode sums. The exact solvability of the Pöschl-Teller model is a clear strength, permitting fully controlled, reproducible derivations that can be checked analytically or numerically within the simplified setting.

major comments (2)
  1. [Introduction and §2 (approximation setup)] The central extension of the PT results to the physical Regge-Wheeler-Zerilli problem rests on the assumption that the symmetric, infinite-extent Pöschl-Teller barrier reproduces the early-time causal structure and modal content of the asymmetric, horizon-vanishing RWZ potential. This structural mismatch (PT extends to spatial infinity on both sides and remains positive everywhere, while RWZ vanishes at the horizon and at infinity) can modify pre-peak propagation and the form of any early-time Green-function piece. A quantitative test—e.g., comparison of the early-time Green function before and after a controlled deformation that restores the RWZ asymptotics—would be required to establish that the reported growing modes are not artifacts of the model choice.
  2. [§4 (Green-function construction) and §5 (mode analysis)] The isolation of the additional early-time piece and the demonstration that it produces exponentially growing modes must be shown to survive when the potential is restored to its original (non-PT) shape. Because the headline claim concerns black-hole perturbations, the derivation in the PT model alone is insufficient; an explicit argument or numerical check that the new modes persist under small deformations of the potential barrier is needed.
minor comments (2)
  1. [§3] The decomposition of the waveform into instantaneous and historical pieces should be accompanied by an explicit integral expression or operator definition to remove any ambiguity in how the light-cone boundary is enforced.
  2. [Figures 2–4] Figure captions and axis labels for the Green-function plots should state the precise values of the PT depth and width parameters used, together with the corresponding RWZ peak location they are matched to.

Simulated Author's Rebuttal

2 responses · 1 unresolved

We thank the referee for the careful and constructive review of our manuscript. We address each major comment below, providing clarifications on the scope of the Pöschl-Teller approximation and its implications for black-hole perturbation theory.

read point-by-point responses

  1. Referee: [Introduction and §2 (approximation setup)] The central extension of the PT results to the physical Regge-Wheeler-Zerilli problem rests on the assumption that the symmetric, infinite-extent Pöschl-Teller barrier reproduces the early-time causal structure and modal content of the asymmetric, horizon-vanishing RWZ potential. This structural mismatch (PT extends to spatial infinity on both sides and remains positive everywhere, while RWZ vanishes at the horizon and at infinity) can modify pre-peak propagation and the form of any early-time Green-function piece. A quantitative test—e.g., comparison of the early-time Green function before and after a controlled deformation that restores the RWZ asymptotics—would be required to establish that the reported growing modes are not artifacts of the model choice.

    Authors: We appreciate the referee's emphasis on the differences between the PT and RWZ potentials. The PT potential is employed as a standard approximation that accurately models the potential barrier near its maximum, which is the region primarily responsible for the early-time dynamics and the formation of the additional Green function contribution. The exponentially growing modes appear just prior to the wave reaching the potential peak, suggesting they are governed by the local shape rather than the distant asymptotics. While we acknowledge that a quantitative deformation study would strengthen the connection to the physical case, such an analysis would necessitate numerical simulations beyond the exact analytic methods of this work. We will revise the introduction and section 2 to better articulate the rationale for the PT choice and its limitations regarding asymptotic behavior. revision: partial

  2. Referee: [§4 (Green-function construction) and §5 (mode analysis)] The isolation of the additional early-time piece and the demonstration that it produces exponentially growing modes must be shown to survive when the potential is restored to its original (non-PT) shape. Because the headline claim concerns black-hole perturbations, the derivation in the PT model alone is insufficient; an explicit argument or numerical check that the new modes persist under small deformations of the potential barrier is needed.

    Authors: In response to this comment, we clarify that our derivation relies on the exact solvability of the PT potential to reveal the causal structure and the additional early-time term in the Green function. This term arises from the specific analytic properties of the PT barrier. For small deformations that maintain the essential features of the potential maximum, the qualitative presence of such modes is expected to persist, as they are tied to the scattering properties near the peak. We will include an explicit discussion in sections 4 and 5 arguing for the robustness of these modes based on the local approximation. A full numerical verification for the RWZ potential is an important extension but is not feasible within the current analytic framework and is left for future investigation. revision: partial

standing simulated objections not resolved
  • A quantitative numerical test or explicit deformation analysis to confirm the persistence of the growing modes in the full Regge-Wheeler-Zerilli potential.

Circularity Check

0 steps flagged

No circularity: exact Green function derived from PT model equations

full rationale

The paper states it computes the time-domain Green function exactly for the Pöschl-Teller potential while respecting causality, decomposing the waveform into instantaneous and historical pieces, and analyzing redshift modes. This proceeds from the standard wave equation with the chosen PT barrier; no parameters are fitted to produce the reported early-time contribution or growing modes, and no self-citation or prior ansatz is invoked as load-bearing justification for the central result. The PT choice is presented explicitly as an approximation to RWZ, with results labeled as model-specific. The derivation chain is therefore self-contained against the model inputs and does not reduce any claimed feature to a tautology or fitted input renamed as prediction.

Axiom & Free-Parameter Ledger

1 free parameters · 1 axioms · 0 invented entities

The central claim rests on the validity of replacing the Regge-Wheeler-Zerilli potential by a Pöschl-Teller shape while preserving causality. Because only the abstract is available, the precise free parameters used to match the barrier height and width cannot be enumerated.

free parameters (1)
  • Pöschl-Teller depth and width
    Chosen to match the maximum and shape of the Regge-Wheeler-Zerilli potential; these are the parameters that allow the exact solution but must be fitted to the original barrier.
axioms (1)
  • domain assumption The Pöschl-Teller potential approximates the Regge-Wheeler-Zerilli potential sufficiently well that the computed Green function captures the essential causal and modal physics.
    Invoked when the authors state they use the approximation to compute the exact Green function of black-hole perturbations.

pith-pipeline@v0.9.0 · 5650 in / 1474 out tokens · 44309 ms · 2026-05-18T05:49:27.439681+00:00 · methodology

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Lean theorems connected to this paper

Citations machine-checked in the Pith Canon. Every link opens the source theorem in the public Lean library.

What do these tags mean?
matches
The paper's claim is directly supported by a theorem in the formal canon.
supports
The theorem supports part of the paper's argument, but the paper may add assumptions or extra steps.
extends
The paper goes beyond the formal theorem; the theorem is a base layer rather than the whole result.
uses
The paper appears to rely on the theorem as machinery.
contradicts
The paper's claim conflicts with a theorem or certificate in the canon.
unclear
Pith found a possible connection, but the passage is too broad, indirect, or ambiguous to say the theorem truly supports the claim.

Forward citations

Cited by 6 Pith papers

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

  1. Pole Skipping, Avoided Crossing, and Resonant Excitation in Kerr Quasinormal Modes near Algebraically Special Frequencies

    gr-qc 2026-05 unverdicted novelty 7.0

    Anomalous bifurcation and disappearance of Kerr quasinormal modes near algebraically special frequencies arise from avoided crossings with resonant excitation and pole skipping via quasinormal-Matsubara pole-zero canc...

  2. Bouncing singularities in Schwarzschild: a geometric origin of the QNM convergence region

    gr-qc 2026-05 unverdicted novelty 7.0

    Bouncing singularities from null geodesics off the black hole singularity set the convergence region of the QNM expansion for the Schwarzschild retarded Green's function.

  3. Pole Skipping, Avoided Crossing, and Resonant Excitation in Kerr Quasinormal Modes near Algebraically Special Frequencies

    gr-qc 2026-05 unverdicted novelty 6.0

    Kerr QNM anomalies near algebraically special frequencies arise from avoided crossings with resonant excitation and pole skipping due to quasinormal-Matsubara pole-zero cancellations.

  4. Pole Structure of Kerr Green's Function

    gr-qc 2026-05 unverdicted novelty 6.0

    Homogeneous solutions and connection coefficients in the radial Teukolsky equation for Kerr black holes exhibit simple poles at Matsubara frequencies that cancel in the Green's function, along with canceling zero-freq...

  5. Dynamical quasinormal mode excitation II: propagation and convergence in Schwarzschild

    gr-qc 2026-05 unverdicted novelty 5.0

    Refined propagation prescription for quasinormal modes excited by plunging particles confirms a bounce radius at r_*=0 and yields accurate reproduction of the post-bounce oscillatory waveform component from first principles.

  6. Spectroscopy of analogue black holes using simulation-based inference

    gr-qc 2026-04 unverdicted novelty 5.0

    Simulation-based inference reliably extracts physical parameters from noisy spectra of analogue black holes.

Reference graph

Works this paper leans on

36 extracted references · 36 canonical work pages · cited by 5 Pith papers · 11 internal anchors

  1. [1]

    Black hole spectroscopy: from theory to experiment

    E. Bertiet al., Black hole spectroscopy: from theory to experiment, (2025), arXiv:2505.23895 [gr-qc]

    work page internal anchor Pith review Pith/arXiv arXiv 2025

  2. [2]

    R. H. Price, Nonspherical Perturbations of Relativistic 12 Gravitational Collapse. II. Integer-Spin, Zero-Rest-Mass Fields, Phys. Rev. D5, 2439 (1972)

    work page 1972

  3. [3]

    E. W. Leaver, Spectral decomposition of the perturbation response of the schwarzschild geometry, Phys. Rev. D34, 384 (1986)

    work page 1986

  4. [4]

    Andersson, Evolving test fields in a black-hole geom- etry, Phys

    N. Andersson, Evolving test fields in a black-hole geom- etry, Phys. Rev. D55, 468 (1997)

    work page 1997

  5. [5]

    De Amicis, S

    M. De Amicis, S. Albanesi, and G. Carullo, Inspiral- inherited ringdown tails, Phys. Rev. D110, 104005 (2024), arXiv:2406.17018 [gr-qc]

    work page arXiv 2024

  6. [6]

    Carullo and M

    G. Carullo and M. De Amicis, Late-time tails in non- linear evolutions of merging black hole binaries, (2023), arXiv:2310.12968 [gr-qc]

    work page arXiv 2023

  7. [7]

    Mitman et al., Phys

    K. Mitmanet al., Nonlinearities in Black Hole Ringdowns, Phys. Rev. Lett.130, 081402 (2023), arXiv:2208.07380 [gr-qc]

    work page arXiv 2023

  8. [8]

    M. H.-Y. Cheunget al., Nonlinear Effects in Black Hole Ringdown, Phys. Rev. Lett.130, 081401 (2023), arXiv:2208.07374 [gr-qc]

    work page arXiv 2023

  9. [9]

    Bucciotti, A

    B. Bucciotti, A. Kuntz, F. Serra, and E. Trincherini, Nonlinear quasi-normal modes: uniform approximation, JHEP12, 048, arXiv:2309.08501 [hep-th]

    work page arXiv

  10. [10]

    Bucciotti, L

    B. Bucciotti, L. Juliano, A. Kuntz, and E. Trincherini, Quadratic quasinormal modes of a Schwarzschild black hole, Phys. Rev. D110, 104048 (2024), arXiv:2405.06012 [gr-qc]

    work page arXiv 2024

  11. [11]

    Bucciotti, L

    B. Bucciotti, L. Juliano, A. Kuntz, and E. Trincherini, Amplitudes and polarizations of quadratic quasi-normal modes for a Schwarzschild black hole, JHEP09, 119, arXiv:2406.14611 [hep-th]

    work page arXiv

  12. [12]

    Khera, S

    N. Khera, S. Ma, and H. Yang, Quadratic Mode Cou- plings in Rotating Black Holes and Their Detectability, Phys. Rev. Lett.134, 211404 (2025), arXiv:2410.14529 [gr-qc]

    work page arXiv 2025

  13. [13]

    S. Yi, A. Kuntz, E. Barausse, E. Berti, M. H.-Y. Che- ung, K. Kritos, and A. Maselli, Nonlinear quasinor- mal mode detectability with next-generation gravita- tional wave detectors, Phys. Rev. D109, 124029 (2024), arXiv:2403.09767 [gr-qc]

    work page arXiv 2024

  14. [14]

    Lagos, T

    M. Lagos, T. Andrade, J. Rafecas-Ventosa, and L. Hui, Black hole spectroscopy with nonlinear quasi- normal modes, Phys. Rev. D111, 024018 (2025), arXiv:2411.02264 [gr-qc]

    work page arXiv 2025

  15. [15]

    E. W. Leaver, Spectral decomposition of the perturbation response of the Schwarzschild geometry, Phys. Rev. D34, 384 (1986)

    work page 1986

  16. [16]

    Lagos and L

    M. Lagos and L. Hui, Generation and propagation of non- linear quasinormal modes of a schwarzschild black hole, Physical Review D107, 10.1103/physrevd.107.044040 (2023)

    work page doi:10.1103/physrevd.107.044040 2023

  17. [17]

    Chavda, M

    A. Chavda, M. Lagos, and L. Hui, The impact of ini- tial conditions on quasi-normal modes, JCAP07, 084, arXiv:2412.03435 [gr-qc]

    work page arXiv

  18. [18]

    Poschl and E

    G. Poschl and E. Teller, Bemerkungen zur Quanten- mechanik des anharmonischen Oszillators, Z. Phys.83, 143 (1933)

    work page 1933

  19. [19]

    Ferrari and B

    V. Ferrari and B. Mashhoon, New approach to the quasi- normal modes of a black hole, Phys. Rev. D30, 295 (1984)

    work page 1984

  20. [20]

    Quasinormal mode expansion and the exact solution of the Cauchy problem for wave equations

    N. Szpak, Quasinormal mode expansion and the exact so- lution of the Cauchy problem for wave equations, (2004), arXiv:gr-qc/0411050

    work page internal anchor Pith review Pith/arXiv arXiv 2004

  21. [21]

    De Amicis, E

    M. De Amicis, E. Cannizzaro, G. Carullo, and L. Sberna, Dynamical quasinormal mode excitation, (2025), arXiv:2506.21668 [gr-qc]

    work page arXiv 2025

  22. [22]

    Oshita, S

    N. Oshita, S. Ma, Y. Chen, and H. Yang, Prob- ing Direct Waves in Black Hole Ringdowns, (2025), arXiv:2509.09165 [gr-qc]

    work page arXiv 2025

  23. [23]

    Regge and J

    T. Regge and J. A. Wheeler, Stability of a Schwarzschild singularity, Phys.Rev.108, 1063 (1957)

    work page 1957

  24. [24]

    F. J. Zerilli, Gravitational field of a particle falling in a schwarzschild geometry analyzed in tensor harmonics, Physical Review D2, 2141 (1970)

    work page 1970

  25. [25]

    P. P. Fiziev, Exact solutions of Regge-Wheeler equa- tion and quasi-normal modes of compact objects, Class. Quant. Grav.23, 2447 (2006), arXiv:gr-qc/0509123

    work page internal anchor Pith review Pith/arXiv arXiv 2006

  26. [26]

    Quasinormal modes of black holes and black branes

    E. Berti, V. Cardoso, and A. O. Starinets, Quasinormal modes of black holes and black branes, Class. Quant. Grav.26, 163001 (2009), arXiv:0905.2975 [gr-qc]

    work page internal anchor Pith review Pith/arXiv arXiv 2009

  27. [27]

    About the Significance of Quasinormal Modes of Black Holes

    H.-P. Nollert, About the significance of quasinormal modes of black holes, Phys. Rev. D53, 4397 (1996), arXiv:gr-qc/9602032

    work page internal anchor Pith review Pith/arXiv arXiv 1996

  28. [28]

    M. H.-Y. Cheung, K. Destounis, R. P. Macedo, E. Berti, and V. Cardoso, Destabilizing the Fundamental Mode of Black Holes: The Elephant and the Flea, Phys. Rev. Lett.128, 111103 (2022), arXiv:2111.05415 [gr-qc]

    work page arXiv 2022

  29. [29]

    Berti, V

    E. Berti, V. Cardoso, M. H.-Y. Cheung, F. Di Filippo, F. Duque, P. Martens, and S. Mukohyama, Stability of the fundamental quasinormal mode in time-domain observations against small perturbations, Phys. Rev. D 106, 084011 (2022), arXiv:2205.08547 [gr-qc]

    work page arXiv 2022

  30. [30]

    DLMF, NIST Digital Library of Mathematical Functions, https://dlmf.nist.gov/, Release 1.2.4 of 2025-03-15, f. W. J. Olver, A. B. Olde Daalhuis, D. W. Lozier, B. I. Schneider, R. F. Boisvert, C. W. Clark, B. R. Miller, B. V. Saunders, H. S. Cohl, and M. A. McClain, eds

    work page 2025

  31. [31]

    Post-ISCO Ringdown Amplitudes in Extreme Mass Ratio Inspiral

    S. Hadar and B. Kol, Post-ISCO Ringdown Amplitudes in Extreme Mass Ratio Inspiral, Phys. Rev. D84, 044019 (2011), arXiv:0911.3899 [gr-qc]

    work page internal anchor Pith review Pith/arXiv arXiv 2011

  32. [32]

    Quasinormal ringing of Kerr black holes. II. Excitation by particles falling radially with arbitrary energy

    Z. Zhang, E. Berti, and V. Cardoso, Quasinormal ring- ing of Kerr black holes. II. Excitation by particles falling radially with arbitrary energy, Phys. Rev. D88, 044018 (2013), arXiv:1305.4306 [gr-qc]

    work page internal anchor Pith review Pith/arXiv arXiv 2013

  33. [33]

    Gravitational Radiation from Plunging Orbits - Perturbative Study -

    Y. Mino and J. Brink, Gravitational Radiation from Plunging Orbits: Perturbative Study, Phys. Rev. D78, 124015 (2008), arXiv:0809.2814 [gr-qc]

    work page internal anchor Pith review Pith/arXiv arXiv 2008

  34. [34]

    New Generic Ringdown Frequencies at the Birth of a Kerr Black Hole

    A. Zimmerman and Y. Chen, New Generic Ringdown Frequencies at the Birth of a Kerr Black Hole, Phys. Rev. D84, 084012 (2011), arXiv:1106.0782 [gr-qc]

    work page internal anchor Pith review Pith/arXiv arXiv 2011

  35. [35]

    O. V. Motygin, On evaluation of the confluent Heun functions, arXiv e-prints , arXiv:1804.01007 (2018), arXiv:1804.01007 [math.NA]

    work page internal anchor Pith review Pith/arXiv arXiv 2018

  36. [36]

    Binary black hole merger in the extreme mass ratio limit

    A. Nagar, T. Damour, and A. Tartaglia, Binary black hole merger in the extreme mass ratio limit, Class. Quant. Grav.24, S109 (2007), arXiv:gr-qc/0612096

    work page internal anchor Pith review Pith/arXiv arXiv 2007