pith. sign in

arxiv: 2606.19435 · v1 · pith:ZNTJXYTKnew · submitted 2026-06-17 · 🌀 gr-qc · hep-th

Deriving effective descriptions and signal predictions for dynamical gravitational systems

Steven B. Giddings , Madhur Mehta This is my paper

Pith reviewed 2026-06-26 19:57 UTC · model grok-4.3

classification 🌀 gr-qc hep-th
keywords effective descriptionsgravitational radiationblack hole modificationsphase shiftsbinary systemscavity actionswave profiles
0
0 comments X

The pith

Cavity boundary actions for black holes connect to observable phase shifts in radiated signals

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

This paper establishes a top-down method for creating effective descriptions of radiation from dynamical gravitational systems such as binary black holes by parameterizing their dynamics with actions on cavity boundaries. It demonstrates how these descriptions link to concrete observables like wave profiles and accumulated phase shifts in emitted signals. The approach is motivated by the need to predict how modifications to classical black hole behavior would appear in gravitational wave data, with phase shifts offering particular sensitivity to small effects during inspiral. Examples use scalar radiation to illustrate the principles, with an outline for extension to gravity.

Core claim

By using an action on the boundaries of cavities that encompass individual bodies in a gravitational system, one derives effective descriptions that systematically connect to radiation observables, including detailed wave profiles and the accumulated phase shift of emitted signals, for classical black holes and models of their modifications.

What carries the argument

The cavity boundary action parameterization, which allows derivation of effective descriptions without cutoff dependence issues and connects them to observable radiation quantities.

If this is right

  • Effective descriptions apply equally to classical black holes and to modified black hole models motivated by quantum mechanics or other new physics.
  • Accumulated phase shifts in signals provide sensitivity to small new effects originating in the inspiral phase.
  • The connection between cavity descriptions and observables holds for scalar radiation and extends to gravitational wave contexts.

Where Pith is reading between the lines

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

  • Applying the cavity method to specific models of modified black holes would yield predicted phase shift signatures for comparison with observations.
  • This could enable top-down predictions of how quantum effects influence gravitational wave signals from binaries.
  • The approach may offer advantages over cutoff-dependent worldline effective field theories in connecting to observables.

Load-bearing premise

Parameterizing the dynamics of bodies with an action defined on cavity boundaries produces a valid effective description that connects to radiation observables.

What would settle it

Computing the radiated signal from a simple binary system and finding that the phase shift does not match the one derived from the cavity action parameters would show the connection does not hold.

Figures

Figures reproduced from arXiv: 2606.19435 by Madhur Mehta, Steven B. Giddings.

Figure 1
Figure 1. Figure 1: Schematic of the cavity description. A region inside an area [PITH_FULL_IMAGE:figures/full_fig_p006_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: For purposes of describing coupling to long-wavelength modes, we expect to be able to [PITH_FULL_IMAGE:figures/full_fig_p009_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Schematic illustration of the energy flux calculations. A moving source, here BH2, [PITH_FULL_IMAGE:figures/full_fig_p015_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Schematic of different scales, associated with emission of radiation governed by effective [PITH_FULL_IMAGE:figures/full_fig_p016_4.png] view at source ↗
read the original abstract

We investigate top-down derivations of effective descriptions for radiation from gravitational systems such as binaries. With a specified cutoff prescription, one can derive worldline effective field theories, but the cutoff dependence also complicates their description. We investigate a related effective approach, based on parameterizing dynamics in terms of an action on the boundaries of cavities encompassing individual bodies. We give examples of such cavity descriptions for black holes and for simple models for modifications of their behavior. We also show how cavity effective descriptions connect to observable quantities -- detailed wave profiles, and importantly, accumulated phase shift of emitted signals. A primary motivation is to have a systematic approach to inferring effects of modification of classical black hole behavior, such as those motivated by the need for black hole evolution to be consistent with quantum mechanics, or by other models for new BH behavior, on gravitational wave signals; the latter phase shifts have in particular been argued to provide sensitivity to small new effects from the inspiral phase. To illustrate basic principles and methods, this paper largely focuses on examples with scalar radiation, but we outline extension of the analysis to gravitational wave contexts.

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 paper investigates top-down derivations of effective descriptions for radiation from gravitational systems such as binaries, using actions parameterized on the boundaries of cavities around individual bodies. It provides examples for black holes and simple modifications using scalar radiation, demonstrates connections between these cavity descriptions and observable quantities including detailed wave profiles and accumulated phase shifts, and outlines an extension to gravitational wave contexts. The motivation is to enable systematic inference of small modifications to classical black hole behavior on gravitational wave signals from the inspiral phase.

Significance. If the cavity boundary action method can be shown to connect systematically to gravitational wave observables without cutoff artifacts, it would provide a principled framework for predicting phase shifts induced by modified black hole dynamics, offering a route to enhanced sensitivity for quantum or other new effects in binary inspirals beyond standard effective field theory approaches.

major comments (2)
  1. [Gravitational wave extension outline] Gravitational wave extension (as outlined in the manuscript): The central claim that cavity effective descriptions yield observable phase shifts for gravitational waves rests on scalar radiation examples, with the tensor mode extension only sketched; no explicit derivation, mode decomposition, or validation against cutoff dependence appears for the Einstein equations or tensor perturbations, which is load-bearing for the stated motivation regarding GW signals.
  2. [Scalar radiation examples and observables] Connection to phase shifts (scalar examples section): While the manuscript states it shows how cavity descriptions connect to accumulated phase shifts, the absence of an explicit formula or numerical example mapping boundary action parameters to the phase accumulation (e.g., via retarded Green's functions or waveform integrals) leaves the claimed observability link unverified in detail even for the scalar case.
minor comments (2)
  1. [Introduction] The title emphasizes 'dynamical gravitational systems' and 'gravitational wave contexts,' yet the body largely restricts to scalar radiation; a brief clarification of scope in the introduction would improve alignment with reader expectations.
  2. Notation for cavity boundaries and cutoff prescriptions could be standardized with a dedicated table or diagram to aid comparison across examples.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their careful review and constructive comments. We address each major point below and indicate the revisions that will be incorporated to strengthen the manuscript.

read point-by-point responses

  1. Referee: Gravitational wave extension (as outlined in the manuscript): The central claim that cavity effective descriptions yield observable phase shifts for gravitational waves rests on scalar radiation examples, with the tensor mode extension only sketched; no explicit derivation, mode decomposition, or validation against cutoff dependence appears for the Einstein equations or tensor perturbations, which is load-bearing for the stated motivation regarding GW signals.

    Authors: We agree that the tensor-mode extension is presented only as an outline. The manuscript's core contribution is the cavity-boundary-action framework illustrated in detail with scalar radiation, which establishes the method and its link to observables; the gravitational-wave sketch is intended to indicate the direct applicability to the Einstein equations rather than to constitute a complete derivation. In the revised manuscript we will expand the outline to include an explicit sketch of the linearized tensor decomposition around the cavity boundary and the corresponding parameterization of the boundary action, while clarifying that a full cutoff-independent validation for gravitational waves lies beyond the present scope. This will better support the stated motivation without overstating the current results. revision: partial

  2. Referee: Connection to phase shifts (scalar examples section): While the manuscript states it shows how cavity descriptions connect to accumulated phase shifts, the absence of an explicit formula or numerical example mapping boundary action parameters to the phase accumulation (e.g., via retarded Green's functions or waveform integrals) leaves the claimed observability link unverified in detail even for the scalar case.

    Authors: We accept that an explicit mapping would make the connection more transparent. Although the manuscript describes the general route from boundary actions through emitted waveforms to phase shifts, we will add in revision an explicit integral expression for the accumulated phase shift in terms of the boundary-action parameters, obtained via the retarded Green's function and the waveform integral. We will also include a concrete numerical illustration for a simple scalar source to demonstrate the mapping. These additions will verify the observability link in detail for the scalar examples. revision: yes

Circularity Check

0 steps flagged

No circularity: top-down derivation and observable connections presented as independent steps

full rationale

The paper describes a cutoff-based derivation of worldline EFTs, then introduces cavity boundary actions as an alternative parameterization, provides explicit examples for black holes and modifications (scalar radiation), and states it shows the connection to wave profiles and accumulated phase shifts. These steps are presented sequentially without any quoted reduction where a 'prediction' equals a fitted input by definition, where a uniqueness theorem is imported from self-citation as load-bearing, or where an ansatz is smuggled via prior work. The gravitational extension is explicitly noted as outlined only, but the scalar derivations remain self-contained against external benchmarks and do not rely on self-referential definitions or renaming of known results.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Abstract-only review provides no identifiable free parameters, axioms, or invented entities; the cutoff prescription and cavity action parameterization are mentioned but not specified in detail.

pith-pipeline@v0.9.1-grok · 5718 in / 1197 out tokens · 41356 ms · 2026-06-26T19:57:34.528053+00:00 · methodology

discussion (0)

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

Reference graph

Works this paper leans on

69 extracted references · 45 linked inside Pith

  1. [1]

    S. W. Hawking,Particle Creation by Black Holes, Commun. Math. Phys.43(1975) 199–220

    1975

  2. [2]

    S. W. Hawking,Breakdown of Predictability in Gravitational Collapse, Phys. Rev. D14 (1976) 2460–2473

    1976

  3. [3]

    D. N. Page,Information in Black Hole Radiation, Phys. Rev. Lett.71(1993) 3743–3746, hep-th/9306083

    Pith/arXiv arXiv 1993

  4. [4]

    S. D. Mathur,The Fuzzball Proposal for Black Holes: An Elementary Review, Fortsch. Phys. 53(2005) 793–827,hep-th/0502050

    Pith/arXiv arXiv 2005

  5. [5]

    S. B. Giddings,Nonviolent unitarization: basic postulates to soft quantum structure of black holes, JHEP12(2017) 047,1701.08765

    Pith/arXiv arXiv 2017

  6. [6]

    Penington, S

    G. Penington, S. H. Shenker, D. Stanford and Z. Yang,Replica wormholes and the black hole interior, JHEP03(2022) 205,1911.11977

    Pith/arXiv arXiv 2022

  7. [7]

    Almheiri, T

    A. Almheiri, T. Hartman, J. Maldacena, E. Shaghoulian and A. Tajdini,Replica Wormholes and the Entropy of Hawking Radiation, JHEP05(2020) 013,1911.12333 25

    Pith/arXiv arXiv 2020

  8. [8]

    Marolf and H

    D. Marolf and H. Maxfield,Transcending the Ensemble: Baby Universes, Spacetime Wormholes, and the Order and Disorder of Black Hole Information, JHEP08(2020) 044, 2002.08950

    arXiv 2020

  9. [9]

    Almheiri, T

    A. Almheiri, T. Hartman, J. Maldacena, E. Shaghoulian and A. Tajdini,The Entropy of Hawking Radiation, Rev. Mod. Phys.93(2021), no. 3, 035002,2006.06872

    arXiv 2021

  10. [10]

    S. B. Giddings,The unitarity crisis, nonviolent unitarization, and implications for quantum spacetime,2412.18650

    arXiv

  11. [11]

    Pretorius,Evolution of Binary Black Hole Spacetimes, Phys

    F. Pretorius,Evolution of Binary Black Hole Spacetimes, Phys. Rev. Lett.95(2005) 121101, gr-qc/0507014

    Pith/arXiv arXiv 2005

  12. [12]

    Campanelli, C

    M. Campanelli, C. O. Lousto, P. Marronetti and Y. Zlochower,Accurate Evolutions of Orbiting Black-Hole Binaries without Excision, Phys. Rev. Lett.96(2006) 111101, gr-qc/0511048

    Pith/arXiv arXiv 2006

  13. [13]

    J. G. Baker, J. Centrella, D.-I. Choi, M. Koppitz and J. van Meter,Gravitational Wave Extraction from an Inspiraling Configuration of Merging Black Holes, Phys. Rev. Lett.96 (2006) 111102,gr-qc/0511103

    Pith/arXiv arXiv 2006

  14. [14]

    Lehner and F

    L. Lehner and F. Pretorius,Numerical Relativity and Astrophysics, Ann. Rev. Astron. Astrophys.52(2014) 661–694,1405.4840

    Pith/arXiv arXiv 2014

  15. [15]

    Blanchet,Gravitational Radiation from Post-Newtonian Sources and Inspiralling Compact Binaries, Living Rev

    L. Blanchet,Gravitational Radiation from Post-Newtonian Sources and Inspiralling Compact Binaries, Living Rev. Rel.17(2014) 2,1310.1528

    Pith/arXiv arXiv 2014

  16. [16]

    Buonanno and T

    A. Buonanno and T. Damour,Effective one-body approach to general relativistic two-body dynamics, Phys. Rev. D59(1999) 084006,gr-qc/9811091

    Pith/arXiv arXiv 1999

  17. [17]

    Buonanno and T

    A. Buonanno and T. Damour,Transition from Inspiral to Plunge in Binary Black Hole Coalescences, Phys. Rev. D62(2000) 064015,gr-qc/0001013

    Pith/arXiv arXiv 2000

  18. [18]

    Damour and A

    T. Damour and A. Nagar,The Effective One Body Description of the Two-Body Problem, Fundam. Theor. Phys.162(2011) 211–252,0906.1769

    Pith/arXiv arXiv 2011

  19. [19]

    W. D. Goldberger and I. Z. Rothstein,An Effective field theory of gravity for extended objects, Phys. Rev. D73(2006) 104029,hep-th/0409156

    Pith/arXiv arXiv 2006

  20. [20]

    W. D. Goldberger and I. Z. Rothstein,Dissipative Effects in the Worldline Approach to Black Hole Dynamics, Phys. Rev. D73(2006) 104030,hep-th/0511133

    Pith/arXiv arXiv 2006

  21. [21]

    W. D. Goldberger and A. Ross,Gravitational Radiative Corrections from Effective Field Theory, Phys. Rev. D81(2010) 124015,0912.4254

    Pith/arXiv arXiv 2010

  22. [22]

    R. A. Porto,Post-Newtonian Corrections to the Motion of Spinning Bodies in NRGR, Phys. Rev. D73(2006) 104031,gr-qc/0511061

    Pith/arXiv arXiv 2006

  23. [23]

    R. A. Porto,The Effective Field Theorist’s Approach to Gravitational Dynamics, Phys. Rept. 633(2016) 1–104,1601.04914 26

    Pith/arXiv arXiv 2016

  24. [24]

    Foffa and R

    S. Foffa and R. Sturani,Effective Field Theory Methods to Model Compact Binaries, Class. Quant. Grav.31(2014) 043001,1309.3474

    Pith/arXiv arXiv 2014

  25. [25]

    Levi,Effective Field Theories of Post-Newtonian Gravity: A Comprehensive Review, Rept

    M. Levi,Effective Field Theories of Post-Newtonian Gravity: A Comprehensive Review, Rept. Prog. Phys.83(2020), no. 7, 075901,1807.01699

    arXiv 2020

  26. [26]

    Cardoso, E

    V. Cardoso, E. Franzin and P. Pani,Is the gravitational-wave ringdown a probe of the event horizon?, Phys. Rev. Lett.116(2016), no. 17, 171101,1602.07309, [Erratum: Phys.Rev.Lett. 117, 089902 (2016)]

    Pith/arXiv arXiv 2016

  27. [27]

    Abedi, H

    J. Abedi, H. Dykaar and N. Afshordi,Echoes from the Abyss: Tentative evidence for Planck-scale structure at black hole horizons, Phys. Rev. D96(2017), no. 8, 082004, 1612.00266

    Pith/arXiv arXiv 2017

  28. [28]

    Cardoso and P

    V. Cardoso and P. Pani,Tests for the existence of black holes through gravitational wave echoes, Nature Astron.1(2017), no. 9, 586–591,1709.01525

    Pith/arXiv arXiv 2017

  29. [29]

    Cardoso and P

    V. Cardoso and P. Pani,Testing the nature of dark compact objects: a status report, Living Rev. Rel.22(2019), no. 1, 4,1904.05363

    Pith/arXiv arXiv 2019

  30. [30]

    Z. Mark, A. Zimmerman, S. M. Du and Y. Chen,A recipe for echoes from exotic compact objects, Phys. Rev. D96(2017), no. 8, 084002,1706.06155

    Pith/arXiv arXiv 2017

  31. [31]

    Maggio, P

    E. Maggio, P. Pani and V. Ferrari,Exotic Compact Objects and How to Quench Their Ergoregion Instability, Phys. Rev. D96(2017), no. 10, 104047,1703.03696

    Pith/arXiv arXiv 2017

  32. [32]

    Maggio, A

    E. Maggio, A. Testa, S. Bhagwat and P. Pani,Analytical Model for Gravitational-Wave Echoes from Spinning Remnants, Phys. Rev. D100(2019), no. 6, 064056,1907.03091

    arXiv 2019

  33. [33]

    Fransen and S

    K. Fransen and S. B. Giddings,Gravitational wave signatures of departures from classical black hole scattering, Phys. Rev. D110(2024), no. 6, 064029,2405.05970

    arXiv 2024

  34. [34]

    E. E. Flanagan and T. Hinderer,Constraining neutron star tidal Love numbers with gravitational wave detectors, Phys. Rev. D77(2008) 021502,0709.1915

    Pith/arXiv arXiv 2008

  35. [35]

    Hinderer,Tidal Love Numbers of Neutron Stars, Astrophys

    T. Hinderer,Tidal Love Numbers of Neutron Stars, Astrophys. J.677(2008) 1216–1220, 0711.2420

    Pith/arXiv arXiv 2008

  36. [36]

    Damour and A

    T. Damour and A. Nagar,Effective One Body Description of Tidal Effects in Inspiralling Compact Binaries, Phys. Rev. D81(2010) 084016,0911.5041

    Pith/arXiv arXiv 2010

  37. [37]

    Datta, R

    S. Datta, R. Brito, S. Bose, P. Pani and S. A. Hughes,Tidal heating as a discriminator for horizons in extreme mass ratio inspirals, Phys. Rev. D101(2020), no. 4, 044004, 1910.07841

    arXiv 2020

  38. [38]

    Maggio, M

    E. Maggio, M. van de Meent and P. Pani,Extreme mass-ratio inspirals around a spinning horizonless compact object, Phys. Rev. D104(2021), no. 10, 104026,2106.07195

    arXiv 2021

  39. [39]

    Sago and T

    N. Sago and T. Tanaka,Efficient search method of anomalous reflection by the central object in an extreme mass-ratio inspiral system by future space gravitational wave detectors, Phys. Rev. D106(2022), no. 2, 024032,2202.04249 27

    arXiv 2022

  40. [40]

    B. C. Seymour and Y. Chen,Gravitational-Wave Signatures of Non-Violent Non-Locality, 2411.13714

    arXiv

  41. [41]

    H. S. Chia, Z. Zhou and M. M. Ivanov,Tidal heating constraints for black holes and exotic compact objects from the LIGO-Virgo-KAGRA data, Phys. Rev. D111(2025), no. 6, 063002, 2404.14641

    arXiv 2025

  42. [42]

    Polchinski,Renormalization and Effective Lagrangians, Nucl

    J. Polchinski,Renormalization and Effective Lagrangians, Nucl. Phys. B231(1984) 269–295

    1984

  43. [43]

    Kosmopoulos, D

    D. Kosmopoulos, D. Perrone and M. Solon,Dynamical Love Numbers for Black Holes and Beyond from Shell Effective Field Theory, Phys. Rev. Lett.136(2026), no. 21, 211401, 2512.04002

    Pith/arXiv arXiv 2026

  44. [44]

    Ronveaux, ed.,Heun’s Differential Equations

    A. Ronveaux, ed.,Heun’s Differential Equations. Oxford University Press, Oxford, 1995

    1995

  45. [45]

    E. W. Leaver,Solutions to a generalized spheroidal wave equation: Teukolsky’s equations in general relativity, and the two-center problem in molecular quantum mechanics, J. Math. Phys.27(1986), no. 5, 1238

    1986

  46. [46]

    P. P. Fiziev,Exact Solutions of Regge-Wheeler Equation and Quasi-Normal Modes of Compact Objects,gr-qc/0509123

    Pith/arXiv arXiv

  47. [47]

    S. Mano, H. Suzuki and E. Takasugi,Analytic Solutions of the Teukolsky Equation and Their Low Frequency Expansions, Prog. Theor. Phys.95(1996) 1079–1096,gr-qc/9603020

    Pith/arXiv arXiv 1996

  48. [48]

    Sasaki and H

    M. Sasaki and H. Tagoshi,Analytic black hole perturbation approach to gravitational radiation, Living Rev. Rel.6(2003) 6,gr-qc/0306120

    Pith/arXiv arXiv 2003

  49. [49]

    R. H. Price and G. Khanna,Gravitational wave sources: reflections and echoes, Class. Quant. Grav.34(2017), no. 22, 225005,1702.04833

    Pith/arXiv arXiv 2017

  50. [50]

    Blanchet,Post-Newtonian Theory for Gravitational Waves, Living Rev

    L. Blanchet,Post-Newtonian Theory for Gravitational Waves, Living Rev. Rel.27(2024) 4

    2024

  51. [51]

    Poisson and M

    E. Poisson and M. Sasaki,Gravitational Radiation from a Particle in Circular Orbit Around a Black Hole. V. Black-Hole Absorption and Tail Corrections, Phys. Rev. D51(1995) 5753–5767,gr-qc/9412027

    Pith/arXiv arXiv 1995

  52. [52]

    Alvi,Energy and Angular Momentum Flow into a Black Hole in a Binary, Phys

    K. Alvi,Energy and Angular Momentum Flow into a Black Hole in a Binary, Phys. Rev. D 64(2001) 104020,gr-qc/0107080

    Pith/arXiv arXiv 2001

  53. [53]

    Poisson,Absorption of Mass and Angular Momentum by Black Holes: Time-Domain Formalisms for Gravitational Perturbations, Phys

    E. Poisson,Absorption of Mass and Angular Momentum by Black Holes: Time-Domain Formalisms for Gravitational Perturbations, Phys. Rev. D70(2004) 084044,gr-qc/0407050

    Pith/arXiv arXiv 2004

  54. [55]

    Datta and S

    S. Datta and S. Bose,Probing the Nature of Central Objects in Extreme-Mass-Ratio Inspirals with Tidal Heating, Phys. Rev. D99(2019), no. 8, 084001,1902.01723 28

    arXiv 2019

  55. [56]

    Binnington and E

    T. Binnington and E. Poisson,Relativistic theory of tidal Love numbers, Phys. Rev. D80 (2009) 084018,0906.1366

    Pith/arXiv arXiv 2009

  56. [57]

    Damour and A

    T. Damour and A. Nagar,Relativistic Tidal Properties of Neutron Stars, Phys. Rev. D80 (2009) 084035,0906.0096

    Pith/arXiv arXiv 2009

  57. [58]

    Cardoso, E

    V. Cardoso, E. Franzin, A. Maselli, P. Pani and G. Raposo,Testing strong-field gravity with tidal Love numbers, Phys. Rev. D95(2017), no. 8, 084014,1701.01116, [Addendum: Phys.Rev.D 95, 089901 (2017)]

    Pith/arXiv arXiv 2017

  58. [59]

    H. S. Chia, T. D. P. Edwards, D. Wadekar, A. Zimmerman, S. Olsen, J. Roulet, T. Venumadhav, B. Zackay and M. Zaldarriaga,In pursuit of Love numbers: First templated search for compact objects with large tidal deformabilities in the LIGO-Virgo data, Phys. Rev. D110(2024), no. 6, 063007,2306.00050

    arXiv 2024

  59. [60]

    W. D. Goldberger, J. Li and I. Z. Rothstein,Non-conservative effects on spinning black holes from world-line effective field theory, JHEP06(2021) 053,2012.14869

    arXiv 2021

  60. [61]

    Taylor and E

    S. Taylor and E. Poisson,Nonrotating black hole in a post-Newtonian tidal environment, Phys. Rev. D78(2008) 084016,0806.3052

    Pith/arXiv arXiv 2008

  61. [62]

    Chatziioannou, E

    K. Chatziioannou, E. Poisson and N. Yunes,Tidal heating and torquing of a Kerr black hole to next-to-leading order in the tidal coupling, Phys. Rev. D87(2013), no. 4, 044022, 1211.1686

    Pith/arXiv arXiv 2013

  62. [63]

    Chatziioannou, E

    K. Chatziioannou, E. Poisson and N. Yunes,Improved next-to-leading order tidal heating and torquing of a Kerr black hole, Phys. Rev. D94(2016), no. 8, 084043,1608.02899

    Pith/arXiv arXiv 2016

  63. [64]

    Skenderis and M

    K. Skenderis and M. Taylor,The Fuzzball Proposal for Black Holes, Phys. Rept.467(2008) 117–171,0804.0552

    Pith/arXiv arXiv 2008

  64. [65]

    Bena and N

    I. Bena and N. P. Warner,Black Holes, Black Rings and Their Microstates, Lect. Notes Phys.755(2008) 1–92,hep-th/0701216

    Pith/arXiv arXiv 2008

  65. [66]

    I. Bena, D. R. Mayerson, A. Puhm and B. Vercnocke,Black Holes as Fuzzballs: A Review, 2204.13113

    arXiv

  66. [67]

    S. R. Coleman,Black Holes as Red Herrings: Topological Fluctuations and the Loss of Quantum Coherence, Nucl. Phys. B307(1988) 867–882

    1988

  67. [68]

    S. B. Giddings and A. Strominger,Loss of Incoherence and Determination of Coupling Constants in Quantum Gravity, Nucl. Phys. B307(1988) 854–866

    1988

  68. [69]

    S. B. Giddings and R. A. Porto,The Gravitational S-matrix, Phys. Rev. D81(2010) 025002, 0908.0004

    Pith/arXiv arXiv 2010

  69. [70]

    K. S. Thorne,Multipole Expansions of Gravitational Radiation, Rev. Mod. Phys.52(1980) 299–339 29

    1980