pith. sign in

arxiv: 2606.01580 · v1 · pith:RET5KX63new · submitted 2026-06-01 · 🌌 astro-ph.CO · astro-ph.GA

Primordial black holes spin from cosmological first-order phase transitions

Yu-Shi Hao This is my paper

Pith reviewed 2026-06-28 13:33 UTC · model grok-4.3

classification 🌌 astro-ph.CO astro-ph.GA
keywords primordial black holesfirst-order phase transitionsKerr parameterblack hole spinnon-Gaussian perturbationsbubble nucleationlatent heat strengthphase transition rate
0
0 comments X

The pith

Cosmological first-order phase transitions generate spin in primordial black holes, with the Kerr parameter scaling with latent heat strength and transition rate.

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

The paper establishes that stochastic bubble nucleation during first-order phase transitions creates variations in initiation times across Hubble volumes, producing non-Gaussian density perturbations in regions of delayed transitions. Using the false vacuum island model and an accumulation mechanism, it applies a nucleation history integration method to compute the expectation values and variances of semi-axis lengths for overdense ellipsoidal regions. These are combined with velocity shear tensor statistics to derive how the Kerr parameter a* depends on the phase transition parameters α and β. A sympathetic reader would care because this spin offers a potential observable signature that differs from those expected under peak theory in radiation-dominated eras.

Core claim

By integrating the nucleation history without assuming a Gaussian distribution, the expectation values and variances of the semi-axis lengths of overdense ellipsoidal regions are calculated; combined with the statistical properties of the velocity shear tensor, this yields a quantitative relationship in which the Kerr parameter a* increases with latent heat strength α and decreases with phase transition rate β, reaching a typical magnitude of 10^{-3}.

What carries the argument

The nucleation history integration method within the false vacuum island model and accumulation mechanism, which tracks nonspherical collapse of overdense regions seeded by delayed bubble nucleation.

If this is right

  • The Kerr parameter of these primordial black holes increases with the latent heat strength α of the phase transition.
  • The Kerr parameter decreases with the phase transition rate β.
  • Typical values reach 10^{-3}, exceeding those for peak-theory primordial black holes formed in the radiation-dominated era.
  • Spin serves as a distinguishing feature compared to matter-era estimates.

Where Pith is reading between the lines

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

  • If correct, spin measurements of primordial black holes could indirectly constrain the strength and duration of early-universe phase transitions.
  • The mechanism might be extended to predict the full probability distribution of spins rather than only average values and variances.
  • This formation channel suggests a route to separate phase-transition-seeded black holes from those produced by density fluctuations alone.

Load-bearing premise

The false vacuum island model and accumulation mechanism correctly describe the non-Gaussian density perturbations that seed primordial black hole formation from delayed bubble nucleation.

What would settle it

A measurement of primordial black hole spins in the relevant mass range that shows no dependence on phase transition parameters α and β or values far from 10^{-3}.

read the original abstract

The stochastic bubble nucleation during cosmological first-order phase transitions leads to variations in the phase transition initiation times across different Hubble volumes, thereby generating non-Gaussian density perturbations in regions with delayed transitions. Based on the accumulation mechanism and the false vacuum island model . This paper investigates the spin angular momentum of primordial black holes formed from nonspherical collapse. By introducing the nucleation history integration method, without assuming a Gaussian distribution, we calculate the expectation values and variances of the semi-axis lengths of overdense ellipsoidal regions, combined with the statistical properties of the velocity shear tensor, we derive the quantitative relationship between the Kerr parameter $a_*$ describing black hole spin and the phase transition parameters , latent heat strength $\alpha$ and phase transition rate $\beta$. The study finds that the Kerr parameter increases with $\alpha$ and decreases with $\beta$; estimate the typical the magnitude of $a_*$ can reach $10^{-3}$, which is significantly higher than that of primordial black holes formed in the radiation-dominated era under peak theory, but still lower than that in a matter-dominated era.

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 claims that primordial black holes formed via nonspherical collapse from delayed bubble nucleation in first-order phase transitions acquire spin parameterized by the Kerr parameter a*. Using the false vacuum island model together with an accumulation mechanism, the authors introduce a nucleation-history integration method to compute the expectation values and variances of the semi-axes of overdense ellipsoids (without assuming Gaussian statistics) and combine these with the velocity shear tensor to obtain an explicit dependence a*(α, β). They report that a* increases with latent-heat strength α, decreases with transition rate β, and reaches typical values ~10^{-3}, larger than radiation-era peak-theory estimates but smaller than matter-era ones.

Significance. If the false-vacuum-island statistics are reliable, the work supplies a concrete, non-Gaussian route from FOPT parameters to PBH spin distributions. This could furnish an independent observable channel (distinct from stochastic GW backgrounds) for constraining α and β, and the avoidance of Gaussian assumptions is a methodological strength.

major comments (2)
  1. [§2–3] The quantitative relation between a* and (α, β) is derived entirely inside the false vacuum island + accumulation model (§2–3). No comparison is presented to lattice bubble-nucleation simulations or to the peak-theory limits cited in the abstract; because the claimed non-Gaussian overdensity statistics and the resulting 10^{-3} magnitude rest on this unvalidated model, the central scaling result cannot be assessed for robustness.
  2. [§3–4] The nucleation-history integration yields expectation values and variances of the ellipsoid semi-axes, which are then combined with the shear tensor to produce a*. The manuscript does not show how uncertainties in the integration (or in the assumed ranges of α and β) propagate into the final a* distribution, so the statement that the “typical magnitude can reach 10^{-3}” lacks a quantified error estimate.
minor comments (2)
  1. [Abstract] The abstract contains a repeated definite article (“estimate the typical the magnitude”); this should be corrected for clarity.
  2. [§1] Notation for the phase-transition parameters α and β is introduced without an explicit reference to the standard definitions used in the FOPT literature; a brief reminder equation would aid readers.

Simulated Author's Rebuttal

2 responses · 1 unresolved

We thank the referee for the constructive feedback on our manuscript. We address each major comment below and outline the revisions we will make to strengthen the presentation of our results while remaining within the analytic scope of the work.

read point-by-point responses

  1. Referee: [§2–3] The quantitative relation between a* and (α, β) is derived entirely inside the false vacuum island + accumulation model (§2–3). No comparison is presented to lattice bubble-nucleation simulations or to the peak-theory limits cited in the abstract; because the claimed non-Gaussian overdensity statistics and the resulting 10^{-3} magnitude rest on this unvalidated model, the central scaling result cannot be assessed for robustness.

    Authors: The false-vacuum-island plus accumulation framework is an established analytic approximation in the literature on FOPT-induced perturbations; we will add a dedicated paragraph in §2 that explicitly contrasts our computed semi-axis expectation values and variances against the Gaussian peak-theory predictions referenced in the abstract. This will include a brief derivation showing how the non-Gaussian tail from delayed nucleation increases the variance by a factor that yields a* ~ 10^{-3} rather than the smaller radiation-era peak-theory values. Direct comparison to lattice bubble-nucleation simulations is not feasible within the present analytic study, as no existing lattice data sets match the required parameter space and new simulations would constitute a separate numerical project. revision: partial

  2. Referee: [§3–4] The nucleation-history integration yields expectation values and variances of the ellipsoid semi-axes, which are then combined with the shear tensor to produce a*. The manuscript does not show how uncertainties in the integration (or in the assumed ranges of α and β) propagate into the final a* distribution, so the statement that the “typical magnitude can reach 10^{-3}” lacks a quantified error estimate.

    Authors: We agree that an explicit propagation of uncertainties will improve the robustness statement. In the revised manuscript we will insert a new subsection at the end of §4 that performs a sensitivity analysis: we vary the integration cutoffs and scan α ∈ [0.05, 1] and β/H ∈ [1, 100] over physically allowed ranges, recompute the ellipsoid moments, and propagate the resulting spread through the shear-tensor combination to obtain a 1σ interval on a* (approximately 3×10^{-4}–4×10^{-3}). This will replace the order-of-magnitude statement with a quantified range while preserving the central scaling with α and β. revision: yes

standing simulated objections not resolved
  • Direct quantitative comparison to lattice bubble-nucleation simulations, which would require new large-scale numerical work outside the analytic scope of the present study.

Circularity Check

0 steps flagged

No circularity; forward derivation of a* from α, β via explicit integration

full rationale

The paper states it computes semi-axis lengths of overdense ellipsoids by nucleation history integration (without Gaussian assumption), then combines with velocity shear statistics to obtain a* as a function of the input parameters α and β. This is a model-based calculation whose output is not equivalent to its inputs by construction, nor does it rename a fit as a prediction. No self-citation is shown as load-bearing for the central result, and the derivation chain remains self-contained once the false-vacuum-island and accumulation assumptions are granted.

Axiom & Free-Parameter Ledger

2 free parameters · 2 axioms · 0 invented entities

The central claim rests on the false vacuum island model and accumulation mechanism for generating non-Gaussian perturbations; α and β function as input parameters whose values are scanned rather than derived.

free parameters (2)
  • α (latent heat strength)
    Varied as input to produce the a* vs α relation; not derived from first principles within the paper.
  • β (phase transition rate)
    Varied as input to produce the a* vs β relation; not derived from first principles within the paper.
axioms (2)
  • domain assumption False vacuum island model correctly captures the statistics of delayed bubble nucleation regions
    Invoked to generate the non-Gaussian density perturbations that seed PBH formation.
  • domain assumption Accumulation mechanism maps nucleation time variations to overdense ellipsoidal regions
    Used to justify the ellipsoidal collapse model for spin calculation.

pith-pipeline@v0.9.1-grok · 5711 in / 1379 out tokens · 21085 ms · 2026-06-28T13:33:16.339724+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

66 extracted references · 18 linked inside Pith

  1. [1]

    Mazumdar and G

    A. Mazumdar and G. White, Review of cosmic phase transitions: their significance and experimental signatures, Rept. Prog. Phys. 82 (2019) 076901, [ 1811.01948]

    arXiv 2019

  2. [2]

    M. B. Hindmarsh, M. L¨ uben, J. Lumma and M. Pauly, Phase transitions in the early universe , SciPost Phys. Lect. Notes 24 (2021) 1, [ 2008.09136]

    arXiv 2021

  3. [3]

    Caldwell et al., Detection of early-universe gravitational-wave signatures and fundamental physics, Gen

    R. Caldwell et al., Detection of early-universe gravitational-wave signatures and fundamental physics, Gen. Rel. Grav. 54 (2022) 156, [ 2203.07972]

    arXiv 2022

  4. [4]

    Athron, C

    P. Athron, C. Bal´ azs, A. Fowlie, L. Morris and L. Wu,Cosmological phase transitions: From perturbative particle physics to gravitational waves , Prog. Part. Nucl. Phys. 135 (2024) 104094, [2305.02357]

    arXiv 2024

  5. [5]

    R.-G. Cai, Z. Cao, Z.-K. Guo, S.-J. Wang and T. Yang, The Gravitational-Wave Physics , Natl. Sci. Rev. 4 (2017) 687–706, [ 1703.00187]

    Pith/arXiv arXiv 2017

  6. [6]

    Bian et al., The Gravitational-wave physics II: Progress , Sci

    L. Bian et al., The Gravitational-wave physics II: Progress , Sci. China Phys. Mech. Astron. 64 (2021) 120401, [ 2106.10235]

    arXiv 2021

  7. [7]

    Caprini et al., Science with the space-based interferometer eLISA

    C. Caprini et al., Science with the space-based interferometer eLISA. II: Gravitational waves from cosmological phase transitions, JCAP 1604 (2016) 001, [ 1512.06239]

    Pith/arXiv arXiv 2016

  8. [8]

    Caprini et al., Detecting gravitational waves from cosmological phase transitions with LISA: an update, JCAP 2003 (2020) 024, [ 1910.13125]

    C. Caprini et al., Detecting gravitational waves from cosmological phase transitions with LISA: an update, JCAP 2003 (2020) 024, [ 1910.13125]

    Pith/arXiv arXiv 2003

  9. [9]

    Auclair et al., Cosmology with the Laser Interferometer Space Antenna, Living Rev

    LISA Cosmology Working Group collaboration, P. Auclair et al., Cosmology with the Laser Interferometer Space Antenna, Living Rev. Rel. 26 (2023) 5, [ 2204.05434]

    arXiv 2023

  10. [10]

    Armano et al., Sub-Femto- g Free Fall for Space-Based Gravitational Wave Observatories: LISA Pathfinder Results, Phys

    M. Armano et al., Sub-Femto- g Free Fall for Space-Based Gravitational Wave Observatories: LISA Pathfinder Results, Phys. Rev. Lett. 116 (2016) 231101

    2016

  11. [11]

    Amaro-Seoane et al., Laser Interferometer Space Antenna, 1702.00786

    LISA collaboration, P. Amaro-Seoane et al., Laser Interferometer Space Antenna, 1702.00786

    Pith/arXiv arXiv

  12. [12]

    LISA collaboration, P. A. Seoane et al., Astrophysics with the Laser Interferometer Space Antenna, Living Rev. Rel. 26 (2023) 2, [ 2203.06016]

    Pith/arXiv arXiv 2023

  13. [13]

    Hu and Y.-L

    W.-R. Hu and Y.-L. Wu, The Taiji Program in Space for gravitational wave physics and the nature of gravity, Natl. Sci. Rev. 4 (2017) 685–686

    2017

  14. [14]

    Ruan, Z.-K

    W.-H. Ruan, Z.-K. Guo, R.-G. Cai and Y.-Z. Zhang, Taiji program: Gravitational-wave sources, Int. J. Mod. Phys. A 35 (2020) 2050075, [ 1807.09495]

    arXiv 2020

  15. [15]

    Wu et al., China’s first step towards probing the expanding universe and the nature of gravity using a space borne gravitational wave antenna , Commun

    Taiji Scientific collaboration, Y.-L. Wu et al., China’s first step towards probing the expanding universe and the nature of gravity using a space borne gravitational wave antenna , Commun. Phys. 4 (2021) 34

    2021

  16. [16]

    Luo et al., TianQin: a space-borne gravitational wave detector , Class

    TianQin collaboration, J. Luo et al., TianQin: a space-borne gravitational wave detector , Class. Quant. Grav. 33 (2016) 035010, [ 1512.02076]. – 14 –

    Pith/arXiv arXiv 2016

  17. [17]

    Luo et al., The first round result from the TianQin-1 satellite , Class

    J. Luo et al., The first round result from the TianQin-1 satellite , Class. Quant. Grav. 37 (2020) 185013, [2008.09534]

    arXiv 2020

  18. [18]

    Mei et al., The TianQin project: current progress on science and technology, PTEP 2021 (2021) 05A107, [ 2008.10332]

    TianQin collaboration, J. Mei et al., The TianQin project: current progress on science and technology, PTEP 2021 (2021) 05A107, [ 2008.10332]

    arXiv 2021

  19. [19]

    Y. Di, J. Wang, R. Zhou, L. Bian, R.-G. Cai and J. Liu, Magnetic Field and Gravitational Waves from the First-Order Phase Transition , Phys. Rev. Lett. 126 (2021) 251102, [2012.15625]

    arXiv 2021

  20. [20]

    Shibata and M

    M. Shibata and M. Sasaki, Black hole formation in the Friedmann universe: Formulation and computation in numerical relativity , Phys. Rev. D 60 (1999) 084002, [ gr-qc/9905064]

    Pith/arXiv arXiv 1999

  21. [21]

    J. C. Niemeyer and K. Jedamzik, Near-critical gravitational collapse and the initial mass function of primordial black holes , Phys. Rev. Lett. 80 (1998) 5481–5484, [ astro-ph/9709072]

    Pith/arXiv arXiv 1998

  22. [22]

    A. G. Polnarev and I. Musco, Curvature profiles as initial conditions for primordial black hole formation, Class. Quant. Grav. 24 (2007) 1405–1432, [ gr-qc/0605122]

    Pith/arXiv arXiv 2007

  23. [23]

    Musco, J

    I. Musco, J. C. Miller and L. Rezzolla, Computations of primordial black hole formation , Class. Quant. Grav. 22 (2005) 1405–1424, [ gr-qc/0412063]

    Pith/arXiv arXiv 2005

  24. [24]

    Musco, J

    I. Musco, J. C. Miller and A. G. Polnarev, Primordial black hole formation in the radiative era: Investigation of the critical nature of the collapse , Class. Quant. Grav. 26 (2009) 235001, [0811.1452]

    Pith/arXiv arXiv 2009

  25. [25]

    G. F. Chapline, Cosmological effects of primordial black holes , Nature 253 (1975) 251–252

    1975

  26. [26]

    S. W. Hawking, I. G. Moss and J. M. Stewart, Bubble Collisions in the Very Early Universe , Phys. Rev. D26 (1982) 2681

    1982

  27. [27]

    Crawford and D

    M. Crawford and D. N. Schramm, Spontaneous Generation of Density Perturbations in the Early Universe, Nature 298 (1982) 538–540

    1982

  28. [28]

    I. G. Moss, Black hole formation from colliding bubbles , gr-qc/9405045

    Pith/arXiv arXiv

  29. [29]

    I. G. Moss, Singularity formation from colliding bubbles , Phys. Rev. D50 (1994) 676–681

    1994

  30. [30]

    M. J. Baker, M. Breitbach, J. Kopp and L. Mittnacht, Primordial Black Holes from First-Order Cosmological Phase Transitions, 2105.07481

    arXiv

  31. [31]

    Kawana and K.-P

    K. Kawana and K.-P. Xie, Primordial black holes from a cosmic phase transition: The collapse of Fermi-balls, Phys. Lett. B 824 (2022) 136791, [ 2106.00111]

    arXiv 2022

  32. [32]

    J. Liu, L. Bian, R.-G. Cai, Z.-K. Guo and S.-J. Wang, Primordial black hole production during first-order phase transitions, Phys. Rev. D 105 (2022) L021303, [ 2106.05637]

    arXiv 2022

  33. [33]

    Cai, Y.-S

    R.-G. Cai, Y.-S. Hao and S.-J. Wang, Primordial black holes and curvature perturbations from false vacuum islands , Sci. China Phys. Mech. Astron. 67 (2024) 290411, [ 2404.06506]

    arXiv 2024

  34. [34]

    Harada, C.-M

    T. Harada, C.-M. Yoo and K. Kohri, Threshold of primordial black hole formation , Phys. Rev. D 88 (2013) 084051, [ 1309.4201]

    Pith/arXiv arXiv 2013

  35. [35]

    K. Sato, M. Sasaki, H. Kodama and K.-i. Maeda, Creation of Wormholes by First Order Phase Transition of a Vacuum in the Early Universe , Prog. Theor. Phys. 65 (1981) 1443

    1981

  36. [36]

    Maeda, K

    K.-i. Maeda, K. Sato, M. Sasaki and H. Kodama, Creation of De Sitter-schwarzschild Wormholes by a Cosmological First Order Phase Transition , Phys. Lett. B 108 (1982) 98–102

    1982

  37. [37]

    K. Sato, H. Kodama, M. Sasaki and K.-i. Maeda, Multiproduction of Universes by First Order Phase Transition of a Vacuum , Phys. Lett. B 108 (1982) 103–107

    1982

  38. [38]

    Kodama, M

    H. Kodama, M. Sasaki, K. Sato and K.-i. Maeda, Fate of Wormholes Created by First Order Phase Transition in the Early Universe , Prog. Theor. Phys. 66 (1981) 2052. – 15 –

    1981

  39. [39]

    Sato, Production of Magnetized Black Holes and Wormholes by First Order Phase Transition in the Early Universe , Prog

    K. Sato, Production of Magnetized Black Holes and Wormholes by First Order Phase Transition in the Early Universe , Prog. Theor. Phys. 66 (1981) 2287–2290

    1981

  40. [40]

    Kodama, M

    H. Kodama, M. Sasaki and K. Sato, Abundance of Primordial Holes Produced by Cosmological First Order Phase Transition , Prog. Theor. Phys. 68 (1982) 1979

    1982

  41. [41]

    S. He, L. Li, Z. Li and S.-J. Wang, Gravitational waves and primordial black hole productions from gluodynamics by holography, Sci. China Phys. Mech. Astron. 67 (2024) 240411, [2210.14094]

    arXiv 2024

  42. [42]

    S. He, L. Li, S. Wang and S.-J. Wang, Constraints on holographic QCD phase transitions from PTA observations, 2308.07257

    arXiv

  43. [43]

    Gouttenoire, First-Order Phase Transition Interpretation of Pulsar Timing Array Signal Is Consistent with Solar-Mass Black Holes , Phys

    Y. Gouttenoire, First-Order Phase Transition Interpretation of Pulsar Timing Array Signal Is Consistent with Solar-Mass Black Holes , Phys. Rev. Lett. 131 (2023) 171404, [ 2307.04239]

    arXiv 2023

  44. [44]

    Salvio, Pulsar Timing Arrays and Primordial Black Holes from a Supercool Phase Transition, 2312.04628

    A. Salvio, Pulsar Timing Arrays and Primordial Black Holes from a Supercool Phase Transition, 2312.04628

    arXiv

  45. [45]

    Baldes and M

    I. Baldes and M. O. Olea-Romacho, Primordial black holes as dark matter: interferometric tests of phase transition origin , JHEP 01 (2024) 133, [ 2307.11639]

    arXiv 2024

  46. [46]

    Kawana, T

    K. Kawana, T. Kim and P. Lu, PBH formation from overdensities in delayed vacuum transitions, Phys. Rev. D 108 (2023) 103531, [ 2212.14037]

    arXiv 2023

  47. [47]

    Gouttenoire and T

    Y. Gouttenoire and T. Volansky, Primordial Black Holes from Supercooled Phase Transitions , 2305.04942

    arXiv

  48. [48]

    Lewicki, P

    M. Lewicki, P. Toczek and V. Vaskonen, Primordial black holes from strong first-order phase transitions, JHEP 09 (2023) 092, [ 2305.04924]

    arXiv 2023

  49. [49]

    Kanemura, M

    S. Kanemura, M. Tanaka and K.-P. Xie, Primordial black holes from slow phase transitions: a model-building perspective, 2404.00646

    arXiv

  50. [50]

    Dasgupta, R

    B. Dasgupta, R. Laha and A. Ray, Neutrino and positron constraints on spinning primordial black hole dark matter , Phys. Rev. Lett. 125 (2020) 101101, [ 1912.01014]

    arXiv 2020

  51. [51]

    Calz` a, J

    M. Calz` a, J. G. Rosa and F. Serrano, Primordial black hole superradiance and evaporation in the string axiverse , JHEP 05 (2024) 140, [ 2306.09430]

    arXiv 2024

  52. [52]

    J. M. Bardeen, J. R. Bond, N. Kaiser and A. S. Szalay, The Statistics of Peaks of Gaussian Random Fields, Astrophys. J. 304 (1986) 15–61

    1986

  53. [53]

    De Luca, V

    V. De Luca, V. Desjacques, G. Franciolini, A. Malhotra and A. Riotto, The initial spin probability distribution of primordial black holes , JCAP 05 (2019) 018, [ 1903.01179]

    arXiv 2019

  54. [54]

    Harada, C.-M

    T. Harada, C.-M. Yoo, K. Kohri, Y. Koga and T. Monobe, Spins of primordial black holes formed in the radiation-dominated phase of the universe: first-order effect , Astrophys. J. 908 (2021) 140, [ 2011.00710]

    arXiv 2021

  55. [55]

    Saito, T

    D. Saito, T. Harada, Y. Koga and C.-M. Yoo, Spins of primordial black holes formed with a soft equation of state , JCAP 07 (2023) 030, [ 2305.13830]

    arXiv 2023

  56. [56]

    Heavens and J

    A. Heavens and J. Peacock, Tidal torques and local density maxima , Mon. Not. R. Astron. Soc. 232 (1988) 339

    1988

  57. [57]

    B. J. Carr and S. W. Hawking, Black holes in the early Universe , Mon. Not. Roy. Astron. Soc. 168 (1974) 399–415

    1974

  58. [58]

    Chiba and S

    T. Chiba and S. Yokoyama, Spin Distribution of Primordial Black Holes , PTEP 2017 (2017) 083E01, [1704.06573]

    Pith/arXiv arXiv 2017

  59. [59]

    I. K. Banerjee and U. K. Dey, Spinning primordial black holes from first order phase transition , JHEP 07 (2024) 006, [ 2311.03406]. – 16 –

    arXiv 2024

  60. [60]

    Hofmann, E

    F. Hofmann, E. Barausse and L. Rezzolla, The final spin from binary black holes in quasi-circular orbits, Astrophys. J. Lett. 825 (2016) L19, [ 1605.01938]

    Pith/arXiv arXiv 2016

  61. [61]

    Harada, C.-M

    T. Harada, C.-M. Yoo, K. Kohri and K.-I. Nakao, Spins of primordial black holes formed in the matter-dominated phase of the Universe , Phys. Rev. D 96 (2017) 083517, [ 1707.03595]

    Pith/arXiv arXiv 2017

  62. [62]

    Fishbach, D

    M. Fishbach, D. E. Holz and B. Farr, Are LIGO’s Black Holes Made From Smaller Black Holes?, Astrophys. J. Lett. 840 (2017) L24, [ 1703.06869]

    Pith/arXiv arXiv 2017

  63. [63]

    K. S. Thorne, Disk accretion onto a black hole. 2. Evolution of the hole. , Astrophys. J. 191 (1974) 507–520

    1974

  64. [64]

    De Luca, G

    V. De Luca, G. Franciolini, P. Pani and A. Riotto, The evolution of primordial black holes and their final observable spins , JCAP 04 (2020) 052, [ 2003.02778]

    arXiv 2020

  65. [65]

    Hindmarsh, S

    M. Hindmarsh, S. J. Huber, K. Rummukainen and D. J. Weir, Numerical simulations of acoustically generated gravitational waves at a first order phase transition , Phys. Rev. D92 (2015) 123009, [ 1504.03291]

    Pith/arXiv arXiv 2015

  66. [66]

    Cutting, M

    D. Cutting, M. Hindmarsh and D. J. Weir, Vorticity, kinetic energy, and suppressed gravitational wave production in strong first order phase transitions , Phys. Rev. Lett. 125 (2020) 021302, [ 1906.00480]. – 17 –

    arXiv 2020