pith. sign in

arxiv: 2605.18428 · v1 · pith:MHFLCQL6new · submitted 2026-05-18 · 🌀 gr-qc · astro-ph.HE

Probing (sub-)solar-mass black holes and superspinars with current and next-generation gravitational-wave observatories

K. S. Sruthy , N. V. Krishnendu , Chandrachur Chakraborty , Nami Uchikata This is my paper

Pith reviewed 2026-05-20 09:00 UTC · model grok-4.3

classification 🌀 gr-qc astro-ph.HE
keywords gravitational wavesblack holessuperspinarsparameter estimationpost-Newtonian waveformsthird-generation detectorssub-solar massspin measurements
0
0 comments X

The pith

Third-generation gravitational-wave detectors can measure the spins of sub-solar-mass compact objects to 10^{-4}--10^{-3} precision.

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

The paper examines the detectability and parameter-estimation prospects for binaries that include black holes or superspinars with masses from 0.1 to 2 solar masses using current and future gravitational-wave observatories. It models the signals with the TaylorF2 post-Newtonian waveform truncated at the innermost stable circular orbit and compares the reach of Advanced LIGO against the Einstein Telescope and Cosmic Explorer. The analysis shows that the improved sensitivity and low-frequency coverage of third-generation detectors yield signal-to-noise ratios of roughly 100 to 350, which in turn permit spin measurements precise enough to observationally separate near-extremal black holes from superspinars. A reader would care because such measurements could test whether objects exist that rotate faster than the black-hole limit and thereby probe both primordial formation channels and the boundaries of general relativity.

Core claim

The central claim is that third-generation observatories achieve spin-parameter uncertainties of order 10^{-4} to 10^{-3} for these low-mass systems at signal-to-noise ratios of 100--350, thereby enabling clear observational discrimination between near-extremal black holes and superspinars in the mass range 0.1--2 solar masses.

What carries the argument

The frequency-domain post-Newtonian inspiral waveform TaylorF2 truncated at the innermost stable circular orbit, which is used both to generate simulated signals and to perform Fisher-matrix or similar parameter estimation for mass and spin.

If this is right

  • Third-generation detectors extend the observable mass range for these binaries and deliver substantially higher signal-to-noise ratios than current instruments.
  • Spin precision at the level of 10^{-4}--10^{-3} would observationally separate objects with dimensionless spin at or below 1 from those with spin greater than 1.
  • The longer inspiral phase captured by improved low-frequency sensitivity supplies many more gravitational-wave cycles and therefore tighter constraints on all binary parameters.
  • Detection of such systems would directly constrain the existence and abundance of sub-solar-mass compact objects from primordial or exotic channels.

Where Pith is reading between the lines

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

  • If superspinars are ruled out at the quoted precision, the result would tighten limits on the maximum rotation rate allowed by general relativity for horizonless objects.
  • The same truncation-at-ISCO strategy could be applied to other waveform families or to full inspiral-merger-ringdown models once they become available for superspinars.
  • Population studies that combine these spin measurements with mass distributions could distinguish primordial formation from high-energy production mechanisms.

Load-bearing premise

The gravitational-wave signals from superspinars can be adequately described by the standard TaylorF2 inspiral waveform truncated at the ISCO without extra modifications arising from their exotic properties.

What would settle it

An actual detection of a sub-solar-mass binary whose recovered primary spin exceeds 1 at more than a few standard deviations, or a failure to reach the quoted spin precision when real data from Einstein Telescope or Cosmic Explorer are analyzed with the same waveform model.

Figures

Figures reproduced from arXiv: 2605.18428 by Chandrachur Chakraborty, K. S. Sruthy, Nami Uchikata, N. V. Krishnendu.

Figure 1
Figure 1. Figure 1: Scatter plot of the network SNR as a function of chirp mass [PITH_FULL_IMAGE:figures/full_fig_p008_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Scatter plot of uncertainty in chirp mass with SNR for HL and 4040ET networks. For further [PITH_FULL_IMAGE:figures/full_fig_p008_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Variation of the uncertainty in the dimensionless aligned spin components of the two collapsed [PITH_FULL_IMAGE:figures/full_fig_p010_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Variation of the uncertainty in the dimensionless aligned spin components of the two collapsed [PITH_FULL_IMAGE:figures/full_fig_p010_4.png] view at source ↗
read the original abstract

Gravitational-wave observations provide a powerful probe of compact objects and strong-field gravity. In this work, we investigate the detectability of binaries containing (sub-)solar-mass black holes and superspinars with current and next-generation gravitational-wave observatories. Such objects may arise from primordial formation channels or from more exotic high-energy scenarios, and their detection would provide important insights into the population of low-mass compact objects and the physics of extreme gravitational fields. We model the gravitational-wave signals using the frequency-domain post-Newtonian inspiral waveform model TaylorF2, and truncate the signal at the innermost stable circular orbit (ISCO) to avoid contamination from the post-inspiral regime. We assess the observability of these systems using the sensitivities of current detectors such as Advanced LIGO and upcoming third-generation observatories including the Einstein Telescope and Cosmic Explorer. Our results show that while current detectors have limited reach for very low-mass binaries, third-generation observatories can enhance both detection capability and parameter-estimation precision. Their improved strain sensitivity and extended low-frequency coverage allow these observatories to track the inspiral phase over a substantially larger number of gravitational-wave cycles. As a result, they achieve considerably higher signal-to-noise ratios and provide dramatically improved constraints on binary parameters. In particular, it is possible to measure the primary spin parameter with precision $\Delta \chi_{1z}~\sim~10^{-4}-10^{-3}$, potentially allowing clear observational discrimination between near-extremal black holes and superspinars in the mass range $0.1~M_\odot-2~M_\odot$ and with signal-to-noise ratio of $\sim 100-350$.

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

1 major / 2 minor

Summary. The paper investigates the detectability of (sub-)solar-mass black holes and superspinars in binaries using current (Advanced LIGO) and next-generation (Einstein Telescope, Cosmic Explorer) gravitational-wave detectors. It models signals with the TaylorF2 post-Newtonian inspiral waveform truncated at the ISCO, computes SNRs and Fisher-matrix parameter uncertainties, and claims that third-generation detectors can achieve primary spin precisions Δχ_{1z} ∼ 10^{-4}–10^{-3} for masses 0.1–2 M_⊙ at SNR ∼100–350, enabling observational discrimination between near-extremal Kerr black holes and superspinars.

Significance. If the waveform truncation and modeling assumptions are valid, the results would be significant for extending GW probes to exotic low-mass compact objects and for showing how 3G detectors' extended low-frequency sensitivity yields high-precision spin measurements over many cycles. The forward-modeling approach using standard noise curves is a positive aspect, but the central discrimination claim depends on unverified applicability to superspinars.

major comments (1)
  1. [Abstract and waveform modeling] Abstract and waveform modeling: the TaylorF2 inspiral is truncated at the Kerr ISCO to obtain the reported Δχ_{1z} ∼ 10^{-4}–10^{-3} precision and discrimination power. For superspinars (|χ| > 1) the effective potential, ISCO radius, and geodesic structure differ from the Kerr case used to derive both the PN coefficients and the cutoff frequency; no additional error budget or modified termination condition is provided. This directly undermines the spin-uncertainty and discrimination claims for the superspinar hypothesis.
minor comments (2)
  1. [Parameter estimation section] Clarify whether the Fisher-matrix analysis includes the full covariance with mass and other parameters or reports marginal errors only.
  2. [Methods] Add explicit statements on the range of validity of TaylorF2 for the quoted mass and frequency bands.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for their careful reading and constructive feedback. We address the major comment on waveform modeling below and will revise the manuscript accordingly to strengthen the presentation of our assumptions and results.

read point-by-point responses

  1. Referee: [Abstract and waveform modeling] Abstract and waveform modeling: the TaylorF2 inspiral is truncated at the Kerr ISCO to obtain the reported Δχ_{1z} ∼ 10^{-4}–10^{-3} precision and discrimination power. For superspinars (|χ| > 1) the effective potential, ISCO radius, and geodesic structure differ from the Kerr case used to derive both the PN coefficients and the cutoff frequency; no additional error budget or modified termination condition is provided. This directly undermines the spin-uncertainty and discrimination claims for the superspinar hypothesis.

    Authors: We agree that the ISCO location for superspinars differs from the Kerr case. However, TaylorF2 is a post-Newtonian inspiral model whose coefficients are determined by the weak-field orbital dynamics at large separations; these coefficients do not depend on the strong-field geodesic structure near the compact object. The truncation at the Kerr ISCO is adopted uniformly to keep the waveform within the regime where the inspiral-only approximation remains valid and to exclude the unmodeled merger phase. For superspinars with |χ| > 1 the ISCO radius is typically smaller than the Kerr value, so the actual signal would contain additional cycles. Consequently, truncating at the Kerr ISCO yields conservative (lower) estimates of both SNR and spin precision; the true measurement uncertainties for superspinars would be at least as good as, and likely better than, the values we report. We will revise the manuscript to add an explicit discussion of this approximation in the waveform section, state that the quoted precisions are conservative lower bounds for superspinars, and note that the discrimination between near-extremal Kerr black holes and superspinars rests on whether the recovered spin lies above or below unity within the reported uncertainties. This clarification will be added without changing the numerical results or main conclusions. revision: yes

Circularity Check

0 steps flagged

No significant circularity; forward modeling with standard assumptions

full rationale

The paper performs a standard Fisher-matrix parameter-estimation study on the TaylorF2 waveform truncated at the Kerr ISCO. The reported spin precision Δχ_{1z} ∼ 10^{-4}–10^{-3} is a direct numerical output of that calculation under the stated modeling choices; it is not obtained by fitting to data and then relabeling the fit as a prediction, nor does any central equation reduce to a self-definition or self-citation chain. The applicability of the Kerr ISCO cutoff to superspinars is an explicit modeling assumption rather than a derived result that loops back on itself. No load-bearing step equates the claimed observable to its own input by construction.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 1 invented entities

The central claim rests on the validity of the TaylorF2 model for these systems and the existence of superspinars as a testable hypothesis.

axioms (2)
  • domain assumption General relativity holds for the spacetime around these objects
    Used to justify the waveform model and ISCO truncation.
  • standard math The post-Newtonian approximation is valid for the inspiral phase up to ISCO
    Basis for TaylorF2 model application.
invented entities (1)
  • superspinars no independent evidence
    purpose: Exotic objects with spin parameter greater than 1 to explore beyond-Kerr physics
    Hypothetical objects introduced as targets for discrimination via spin measurements.

pith-pipeline@v0.9.0 · 5860 in / 1546 out tokens · 46778 ms · 2026-05-20T09:00:10.565122+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.

Reference graph

Works this paper leans on

88 extracted references · 88 canonical work pages · 12 internal anchors

  1. [1]

    The detectors are modeled using their design sensitivity power spectral densities

    Second-Generation Detector Network We consider a two-detector network consisting of the Advanced LIGO observatories at Hanford (LHO) and Livingston (LLO), hereafter referred to as the HL network. The detectors are modeled using their design sensitivity power spectral densities. Within the GWBENCH framework [42], these are denoted as aLIGO H and aLIGO L

    work page

  2. [2]

    The CE detectors are assumed to be L- shaped interferometers with 40 km arm length (CE-

    Third-Generation Detector Network For the third-generation configuration, we consider a three-detector network composed of two Cosmic Ex- plorer (CE) interferometers and one Einstein Tele- scope (ET). The CE detectors are assumed to be L- shaped interferometers with 40 km arm length (CE-

    work page

  3. [3]

    Since their final locations are not yet fixed, we place them at the current LIGO Hanford and Liv- ingston sites with the same orientations

    [29]. Since their final locations are not yet fixed, we place them at the current LIGO Hanford and Liv- ingston sites with the same orientations. These are denoted as CE-40 H and CE-40 L in GWBENCH [42]. Network Number of Detectors Name XG Observatories in Network HL 0 (2G only) aLIGO H, aLIGO L 4040ET 3 (XG) CE-40 H, CE-40 L, ET V TABLE I: Detector netwo...

    work page

  4. [4]

    The detectability of a gravitational-wave signal and the precision with which its parameters can be measured depend primarily on the signal-to-noise ratio (SNR),ρ

    Signal-to-Noise Ratio and Detection Criteria Having described the detector network configu- rations and the simulated binary population, we now outline the parameter-estimation framework employed in this work. The detectability of a gravitational-wave signal and the precision with which its parameters can be measured depend primarily on the signal-to-nois...

    work page

  5. [5]

    Fisher Matrix Formalism To estimate parameter uncertainties, we employ the Fisher information matrix formalism. For a given de- 6 tector, the Fisher information matrix Γ ab which is re- lated to the derivatives of the waveform with respect to the set of source parametersλis defined as: Γab = 2 Z fupper flow ˜hA,a˜h∗ A,b + ˜h∗ A,a˜hA,b SAn d f,(3) where∗co...

    work page arXiv 1982

  6. [6]

    The third body carries away the excess energy, allowing the remaining pair to form a bound binary

    Three-body Binary Formation In dense stellar systems, binaries can form dynami- cally through three-body encounters, in which two ini- tially unbound objects become gravitationally bound by transferring excess kinetic energy to a third pass- ing object. The third body carries away the excess energy, allowing the remaining pair to form a bound binary. This...

    work page

  7. [7]

    Binary Exchange Interactions Exchange interactions require the presence of a pre- existing binary population. However, binaries in the central parsec of the Galaxy are expected to be effi- ciently disrupted by dynamical encounters and tidal perturbations from the central supermassive black hole, Sgr A* [78, 79]. The dynamical evolution of binaries in such...

    work page

  8. [8]

    The capture cross section was derived in [64], which is given by Eq

    Two-Body Gravitational-wave Capture Two initially unbound compact objects may form a binary if sufficient orbital energy is radiated during a close encounter. The capture cross section was derived in [64], which is given by Eq. (6). The corresponding binary formation timescale can be estimated as, t= 1 nσcapv ∼10 32 s∼1.3×10 24 s∼4.4×10 16 yr. This timesc...

    work page

  9. [9]

    B. P. Abbott et al. (LIGO Scientific Collaboration and Virgo Collaboration), Phys. Rev. Lett.116, 061102 (2016)

    work page 2016

  10. [10]

    Abac et al., apjl995, L18 (2025)

    A. Abac et al., apjl995, L18 (2025)

    work page 2025

  11. [11]

    A. G. Abac et al. (LIGO Scientific, VIRGO, KAGRA) (2025), 2508.18081

    work page internal anchor Pith review Pith/arXiv arXiv 2025

  12. [12]

    A. G. Abac et al. (LIGO Scientific, VIRGO, KAGRA) (2025), 2508.18082

    work page internal anchor Pith review Pith/arXiv arXiv 2025

  13. [13]

    A. G. Abac et al. (LIGO Scientific, VIRGO, KAGRA) (2026), 2603.19019

    work page internal anchor Pith review Pith/arXiv arXiv 2026

  14. [14]

    A. G. Abac et al. (LIGO Scientific, VIRGO, KAGRA) (2026), 2603.19020

    work page internal anchor Pith review Pith/arXiv arXiv 2026

  15. [15]

    A. G. Abac et al. (LIGO Scientific, VIRGO, KAGRA) (2026), 2603.19021

    work page internal anchor Pith review Pith/arXiv arXiv 2026

  16. [16]

    A. G. Abac et al. (LIGO Scientific, Virgo, KAGRA), Phys. Rev. Lett.135, 111403 (2025), 2509.08054

    work page internal anchor Pith review Pith/arXiv arXiv 2025

  17. [17]

    R. P. Kerr, Phys. Rev. Lett.11, 237 (1963)

    work page 1963

  18. [18]

    Chakraborty, P

    C. Chakraborty, P. Kocherlakota, and P. S. Joshi, Phys. Rev. D95, 044006 (2017)

    work page 2017

  19. [19]

    Chakraborty, P

    C. Chakraborty, P. Kocherlakota, M. Patil, S. Bhat- tacharyya, P. S. Joshi, and A. Kr´ olak, Phys. Rev. D 95, 084024 (2017)

    work page 2017

  20. [20]

    E. G. Gimon and P. Hoˇ rava, Physics Letters B672, 299 (2009)

    work page 2009

  21. [21]

    Chakraborty and S

    C. Chakraborty and S. Bhattacharyya, Journal of Cosmology and Astroparticle Physics2024, 007 (2024)

    work page 2024

  22. [22]

    Patil et al., Phys

    M. Patil et al., Phys. Rev. D93, 104015 (2016)

    work page 2016

  23. [23]

    Bambi et al., Phys

    C. Bambi et al., Phys. Rev. D100, 044057 (2019)

    work page 2019

  24. [24]

    M. Wade, J. D. E. Creighton, E. Ochsner, and A. B. Nielsen, Phys. Rev. D88, 083002 (2013)

    work page 2013

  25. [25]

    Prunier et al., Physics of the Dark Universe46, 14 101582 (2024)

    M. Prunier et al., Physics of the Dark Universe46, 14 101582 (2024)

    work page 2024

  26. [26]

    Morr´ as et al., Physics of the Dark Universe42, 101285 (2023)

    G. Morr´ as et al., Physics of the Dark Universe42, 101285 (2023)

    work page 2023

  27. [27]

    Implications for Primordial Black Hole Dark Matter from a Single Subsolar Mass Gravitational-wave Detection in LVK O1--O4

    A. Magaraggia and N. Cappelluti (2026), 2602.21295

    work page internal anchor Pith review Pith/arXiv arXiv 2026

  28. [28]

    B. P. Abbott et al., apjl892, L3 (2020)

    work page 2020

  29. [29]

    Abbott et al., apjl896, L44 (2020)

    R. Abbott et al., apjl896, L44 (2020)

    work page 2020

  30. [30]

    Dasgupta, R

    B. Dasgupta, R. Laha, and A. Ray, Phys. Rev. Lett. 126, 141105 (2021)

    work page 2021

  31. [31]

    Density Perturbations and Black Hole Formation in Hybrid Inflation

    J. Garcia-Bellido, A. D. Linde, and D. Wands, Phys. Rev. D54, 6040 (1996), astro-ph/9605094

    work page internal anchor Pith review Pith/arXiv arXiv 1996

  32. [32]

    S. W. Hawking, Physics Letters B231:3(1989)

    work page 1989

  33. [33]

    S. W. Hawking, I. G. Moss, and J. M. Stewart, Phys. Rev. D26, 2681 (1982)

    work page 1982

  34. [34]

    Chakraborty, S

    C. Chakraborty, S. Bhattacharyya, and P. S. Joshi, J. Cosmol. Astropart. Phys.2024, 053 (2024)

    work page 2024

  35. [35]

    Punturo et al., Classical and Quantum Gravity 27, 194002 (2010)

    M. Punturo et al., Classical and Quantum Gravity 27, 194002 (2010)

    work page 2010

  36. [36]

    Hild et al., Classical and Quantum Gravity28, 094013 (2011)

    S. Hild et al., Classical and Quantum Gravity28, 094013 (2011)

    work page 2011

  37. [37]

    Cosmic Explorer: The U.S. Contribution to Gravitational-Wave Astronomy beyond LIGO

    D. Reitze et al. (2019), 1907.04833

    work page internal anchor Pith review Pith/arXiv arXiv 2019

  38. [38]

    N. E. Wolfe, S. Vitale, and C. Talbot, JCAP11, 039 (2023)

    work page 2023

  39. [39]

    Golomb, I

    J. Golomb, I. Legred, K. Chatziioannou, A. Abac, and T. Dietrich, Phys. Rev. D110, 063014 (2024)

    work page 2024

  40. [40]

    D. N. Page, Phys. Rev. D13, 198 (1976)

    work page 1976

  41. [41]

    Chakraborty and S

    C. Chakraborty and S. Bhattacharyya, Physical Re- view D106, 103028 (2022)

    work page 2022

  42. [42]

    Mirbabayi, A

    M. Mirbabayi, A. Gruzinov, and J. Nore˜ na, Journal of Cosmology and Astroparticle Physics2020, 017 (2020)

    work page 2020

  43. [43]

    V. D. Luca et al., Journal of Cosmology and Astropar- ticle Physics2020, 044 (2020)

    work page 2020

  44. [44]

    S. D. McDermott, H.-B. Yu, and K. M. Zurek, Phys. Rev. D85, 023519 (2012)

    work page 2012

  45. [45]

    H. A. Adarsha, C. Chakraborty, and S. Bhat- tacharyya, Phys. Rev. D111, 103033 (2025)

    work page 2025

  46. [46]

    H. A. Adarsha, C. Chakraborty, and S. Bhat- tacharyya, The European Physical Journal C86, 278 (2026)

    work page 2026

  47. [47]

    W. E. East and L. Lehner, Phys. Rev. D100, 124026 (2019)

    work page 2019

  48. [48]

    Uchikata and T

    N. Uchikata and T. Narikawa, Phys. Rev. D104, 024059 (2021)

    work page 2021

  49. [49]

    Guptaet al., Classical and Quantum Gravity41, 245001 (2024), arXiv:2307.10421 [gr-qc]

    I. Gupta et al. (2024), 2307.10421

    work page arXiv 2024

  50. [50]

    Borhanian,GWBENCH: a novel Fisher information package for gravitational-wave benchmarking,Class

    S. Borhanian (2020), 2010.15202

    work page arXiv 2020

  51. [51]

    Cutler and E

    C. Cutler and E. E. Flanagan, Phys. Rev. D49, 2658 (1994)

    work page 1994

  52. [52]

    Borhanian, Classical and Quantum Gravity38, 175014 (2021)

    S. Borhanian, Classical and Quantum Gravity38, 175014 (2021)

    work page 2021

  53. [53]

    LIGO Scientific Collaboration, Virgo Col- laboration, and KAGRA Collaboration, LVK Algorithm Library - LALSuite, Free software (GPL) (2018)

    work page 2018

  54. [54]

    Favata, C

    M. Favata, C. Kim, K. Arun, J. Kim, and H. W. Lee, Physical Review D105, 023003 (2022)

    work page 2022

  55. [55]

    B. S. Sathyaprakash and S. V. Dhurandhar, Phys. Rev. D44, 3819 (1991)

    work page 1991

  56. [56]

    B. R. I. T. Damour and B. S. Sathyaprakash, Phys. Rev. D57, 885 (1998)

    work page 1998

  57. [57]

    K. G. A. et al., Phys. Rev. D71, 084008 (2005)

    work page 2005

  58. [58]

    B. P. Abbott et al. (LIGO Scientific and Virgo Col- laboration), Phys. Rev. Lett.118, 221101 (2017)

    work page 2017

  59. [59]

    B. P. Abbott et al. (LIGO Scientific Collaboration and Virgo Collaboration), Phys. Rev. Lett.119, 141101 (2017)

    work page 2017

  60. [60]

    B. P. Abbott et al., apjl851, L35 (2017), 1711.05578

    work page internal anchor Pith review Pith/arXiv arXiv 2017

  61. [61]

    B. P. Abbott et al., Phys. Rev. X9, 031040 (2019)

    work page 2019

  62. [62]

    Abbott et al., Phys

    R. Abbott et al., Phys. Rev. D102, 043015 (2020)

    work page 2020

  63. [63]

    Abbott et al., Phys

    R. Abbott et al., Phys. Rev. Lett.125, 101102 (2020)

    work page 2020

  64. [64]

    Abbott et al., The Astrophysical Journal

    R. Abbott et al., The Astrophysical Journal. Letters (Online)900(2020)

    work page 2020

  65. [65]

    Abbott et al

    R. Abbott et al. (LIGO Scientific Collaboration and Virgo Collaboration), Phys. Rev. X11, 021053 (2021)

    work page 2021

  66. [66]

    Biscoveanu, M

    S. Biscoveanu, M. Isi, S. Vitale, and V. Varma, Phys. Rev. Lett.126, 171103 (2021)

    work page 2021

  67. [67]

    C. V. D. Broeck and A. S. Sengupta, Classical and Quantum Gravity24, 1089 (2007)

    work page 2007

  68. [68]

    Favata, C

    M. Favata, C. Kim, K. G. Arun, J. Kim, and H. W. Lee, Phys. Rev. D105, 023003 (2022)

    work page 2022

  69. [69]

    L. S. Finn, Phys. Rev. D46, 5236 (1992)

    work page 1992

  70. [70]

    Chandrasekhar, Fundam

    S. Chandrasekhar, Fundam. Theor. Phys.9, 5 (1984)

    work page 1984

  71. [71]

    Poisson and C

    E. Poisson and C. M. Will, Phys. Rev. D52, 848 (1995)

    work page 1995

  72. [72]

    G. D. Quinlan and S. L. Shapiro, ApJ343, 725 (1989)

    work page 1989

  73. [73]

    R. M. O’Leary, B. Kocsis, and A. Loeb, MNRAS395, 2127 (2009)

    work page 2009

  74. [74]

    Bird et al., Phys

    S. Bird et al., Phys. Rev. Lett.116, 201301 (2016)

    work page 2016

  75. [75]

    LCDM-based models for the Milky Way and M31 I: Dynamical Models

    A. Klypin, H. Zhao, and R. S. Somerville, Astrophys. J.573, 597 (2002), astro-ph/0110390

    work page internal anchor Pith review Pith/arXiv arXiv 2002

  76. [76]

    X. X. Xue et al., apj684, 1143 (2008)

    work page 2008

  77. [77]

    Sartore, E

    N. Sartore, E. Ripamonti, A. Treves, and R. Turolla, Astronomy and Astrophysics510, A23 (2010)

    work page 2010

  78. [78]

    B. T. Reed, A. Deibel, and C. J. Horowitz, The As- trophysical Journal921, 89 (2021)

    work page 2021

  79. [79]

    Fontaine, P

    G. Fontaine, P. Brassard, and P. Bergeron, pasp113, 409 (2001)

    work page 2001

  80. [80]

    Binney and S

    J. Binney and S. Tremaine, Galactic Dynamics: Second Edition (2008)

    work page 2008

Showing first 80 references.