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arxiv: 2511.00307 · v1 · submitted 2025-10-31 · 🌀 gr-qc · astro-ph.HE

Spin-up and mass-gain in hyperbolic encounters of spinning black holes

Healey Kogan , Frederick C.L. Pardoe , Helvi Witek This is my paper

Pith reviewed 2026-05-18 01:56 UTC · model grok-4.3

classification 🌀 gr-qc astro-ph.HE
keywords black hole spinshyperbolic encountersnumerical relativitygravitational wavesspin-upmass gainscattering black holesthreshold angle
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The pith

Equal-mass spinning black holes in hyperbolic encounters can gain up to 0.3 in spin and 15 percent in mass by reabsorbing gravitational-wave energy and angular momentum.

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

Numerical relativity simulations of equal-mass black holes with initial spins from -0.7 to 0.7 on hyperbolic trajectories show that the black holes spin up and gain mass most strongly when the encounter is close to the threshold separating scattering from merger. The largest effects appear with high initial momenta and anti-aligned spins. At the threshold angle the spin-up decreases linearly with the starting spin value, and configurations that begin with spin 0.7 can end with lower spin because the mass increase outruns the angular-momentum gain. A reader would care because these changes alter the spin and mass distributions of black holes that scatter rather than merge in dense stellar environments and must be accounted for in gravitational-wave predictions.

Core claim

In hyperbolic encounters, equal-mass black holes re-absorb orbital angular momentum and energy that was radiated in gravitational waves, producing a net spin-up and mass increase. Across the simulation suite the maximum spin-up reaches 0.3 while the mass grows by as much as 15 percent. The effect is strongest near the critical incident angle, large momenta, and negative initial spins. When measured at the threshold angle the spin-up falls linearly with initial spin. Systems that start with spin 0.7 sometimes show a final spin lower than the initial value because the fractional mass gain reduces the dimensionless spin even though the absolute angular momentum has risen.

What carries the argument

Numerical relativity simulations of equal-mass black-hole pairs on hyperbolic trajectories that evolve the full nonlinear Einstein equations and extract the final black-hole mass and spin after the encounter.

If this is right

  • Spin-up is largest for anti-aligned initial spins and impact parameters near the merger threshold.
  • At the threshold angle the spin-up obeys a linear relation with initial spin.
  • High initial spin can produce net spin-down once the mass increase is included.
  • Mass can increase by up to 15 percent in the same near-threshold, high-momentum, anti-aligned encounters.
  • These modifications must be included in models of black-hole spin distributions after repeated scattering events.

Where Pith is reading between the lines

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

  • The linear trend at threshold may permit a simple approximate analytic description of the spin change.
  • Mass and spin modifications of this size would shift expected gravitational-wave signals from black-hole scattering in galactic nuclei.
  • Extending the study to unequal masses or misaligned spins would show whether the same scaling relations persist.
  • A 15 percent mass gain sets a concrete scale for non-merging growth in a single encounter.

Load-bearing premise

The numerical relativity simulations accurately capture the full nonlinear dynamics and radiation without significant truncation errors or artifacts from initial data construction for the chosen range of incident angles and momenta.

What would settle it

A new high-resolution simulation of a near-threshold encounter with initial spin 0.7 that measures whether the final dimensionless spin is lower than the initial value would directly test the reported spin-down effect.

Figures

Figures reproduced from arXiv: 2511.00307 by Frederick C.L. Pardoe, Healey Kogan, Helvi Witek.

Figure 1
Figure 1. Figure 1: FIG. 1. Initial conditions of binary BHs with equal initial [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. Trajectory and gravitational waveform of BH binaries with initial spin [PITH_FULL_IMAGE:figures/full_fig_p006_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. Trajectory and gravitational waveform of BH binaries with initial spin [PITH_FULL_IMAGE:figures/full_fig_p006_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. Threshold angle, [PITH_FULL_IMAGE:figures/full_fig_p007_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5. Evolutions of the BH mass, [PITH_FULL_IMAGE:figures/full_fig_p007_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6. Change in the (dimensionless) spin (top panels) and BH angular momentum (bottom panels) of scattering BHs as a [PITH_FULL_IMAGE:figures/full_fig_p008_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: FIG. 7. Change in spin as a function of the initial spin of BHs [PITH_FULL_IMAGE:figures/full_fig_p009_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: FIG. 8. Change in the (dimensionless) spin (top panel) and BH angular momentum (bottom panel) of scattering BHs as a [PITH_FULL_IMAGE:figures/full_fig_p010_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: FIG. 9. Spin-up efficiency, Eq [PITH_FULL_IMAGE:figures/full_fig_p011_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: FIG. 10. Relative change in the BH mass (top panels) and irreducible mass (bottom panels) of scattering BHs as a function of [PITH_FULL_IMAGE:figures/full_fig_p012_10.png] view at source ↗
Figure 11
Figure 11. Figure 11: FIG. 11. Relative change in the BH mass (solid lines) and [PITH_FULL_IMAGE:figures/full_fig_p012_11.png] view at source ↗
Figure 12
Figure 12. Figure 12: FIG. 12. Relative change in the BH mass (top panel) and irreducible mass (bottom panel) of scattering BHs as a function of [PITH_FULL_IMAGE:figures/full_fig_p013_12.png] view at source ↗
Figure 13
Figure 13. Figure 13: FIG. 13. Relative change in the BH mass (solid lines) and [PITH_FULL_IMAGE:figures/full_fig_p013_13.png] view at source ↗
Figure 15
Figure 15. Figure 15: FIG. 15. Convergence plot (top panels) and percent error [PITH_FULL_IMAGE:figures/full_fig_p015_15.png] view at source ↗
Figure 14
Figure 14. Figure 14: FIG. 14. Convergence plot of the gravitational radiation [PITH_FULL_IMAGE:figures/full_fig_p015_14.png] view at source ↗
Figure 16
Figure 16. Figure 16: FIG. 16. Convergence plot (top panels) and percent error [PITH_FULL_IMAGE:figures/full_fig_p016_16.png] view at source ↗
Figure 17
Figure 17. Figure 17: FIG. 17. Convergence plot (top panels) and percent error [PITH_FULL_IMAGE:figures/full_fig_p016_17.png] view at source ↗
Figure 20
Figure 20. Figure 20: FIG. 20. Convergence plot (top panels) and percent error [PITH_FULL_IMAGE:figures/full_fig_p017_20.png] view at source ↗
Figure 19
Figure 19. Figure 19: FIG. 19. Convergence plot (top panels) and percent error [PITH_FULL_IMAGE:figures/full_fig_p017_19.png] view at source ↗
Figure 21
Figure 21. Figure 21: FIG. 21. Convergence plot of the gravitational radiation in a [PITH_FULL_IMAGE:figures/full_fig_p018_21.png] view at source ↗
Figure 23
Figure 23. Figure 23: FIG. 23. Convergence plot (top panels) and percent error [PITH_FULL_IMAGE:figures/full_fig_p018_23.png] view at source ↗
Figure 22
Figure 22. Figure 22: FIG. 22. Convergence plots (top panels) and percent error [PITH_FULL_IMAGE:figures/full_fig_p018_22.png] view at source ↗
read the original abstract

Scattering black holes spin up and gain mass through the re-absorption of orbital angular momentum and energy radiated in gravitational waves during their encounter. In this work, we perform a series of numerical relativity simulations to investigate the spin-up and mass-gain for equal-mass black holes with a wide range of equal initial spins, $\chi_{\rm i}\in[-0.7,0.7]$, aligned (or anti-aligned) to the orbital angular momentum. We also consider a variety of initial momenta. Furthermore, we explore a range of incident angles and identify the threshold between scattering and merging configurations. The spin-up and mass-gain are typically largest in systems with incident angles close to the threshold value, large momenta, and negative (i.e. anti-aligned) initial spins. When evaluated at the threshold angle, we find that the spin-up decreases linearly with initial spin. Intriguingly, systems with initial spin $\chi_{\rm i}=0.7$ sometimes experience a spin-down, in spite of an increase in the black-hole angular momentum, due to a corresponding gain in the black-hole mass. Across the simulation suite, we find a maximum spin-up of $0.3$ and a maximum increase in the black-hole mass of $15\%$.

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 reports numerical relativity simulations of hyperbolic encounters between equal-mass black holes with initial spins χ_i ∈ [-0.7, 0.7] aligned or anti-aligned with the orbital angular momentum. It quantifies spin-up and mass-gain arising from re-absorption of gravitational-wave radiated angular momentum and energy, maps the threshold incident angle separating scattering from merger, and finds that both effects are maximized near threshold for large initial momenta and negative initial spins. At the threshold angle the spin-up decreases linearly with initial spin; for χ_i = 0.7 some configurations exhibit spin-down despite net angular-momentum gain because of the accompanying mass increase. Across the suite the largest reported values are a spin-up of 0.3 and a 15 % mass increase.

Significance. If the extracted horizon quantities are numerically robust, the results supply concrete benchmarks for the nonlinear strong-field dynamics of spinning black-hole scattering. Such data are relevant for gravitational-wave modeling of high-velocity encounters and for testing general relativity in regimes inaccessible to post-Newtonian or effective-one-body approximations. The systematic scan over spin, momentum, and angle strengthens the potential utility of the findings.

major comments (2)
  1. [Abstract and §4] Abstract and §4 (Results): The headline quantitative claims—maximum spin-up of 0.3 and 15 % mass gain—are extracted from apparent-horizon quantities near the threshold angle. No convergence tests, Richardson extrapolation, or error budgets are reported for these configurations, where curvature and radiation are strongest and truncation errors are most likely to bias the re-absorbed energy and angular momentum. This omission directly affects the reliability of the stated maxima and the linear trend.
  2. [§3] §3 (Numerical setup): The manuscript must document the grid resolutions employed, the location of outer boundaries, and any tests of initial-data gauge or constraint-violation effects. Without these, it is impossible to assess whether the reported spin and mass changes for the closest-to-threshold runs are free of systematic numerical artifacts.
minor comments (2)
  1. [Introduction] Notation for the incident angle and threshold angle should be defined explicitly in the introduction or methods section before their first quantitative use.
  2. [Figures] Figure captions should state the resolution and extraction radius used for the horizon quantities shown.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their thorough review and constructive feedback on our manuscript. We address each of the major comments below and have made revisions to improve the documentation and validation of our numerical results.

read point-by-point responses

  1. Referee: [Abstract and §4] Abstract and §4 (Results): The headline quantitative claims—maximum spin-up of 0.3 and 15 % mass gain—are extracted from apparent-horizon quantities near the threshold angle. No convergence tests, Richardson extrapolation, or error budgets are reported for these configurations, where curvature and radiation are strongest and truncation errors are most likely to bias the re-absorbed energy and angular momentum. This omission directly affects the reliability of the stated maxima and the linear trend.

    Authors: We agree that convergence tests and error estimates are essential for establishing the reliability of the quantitative results, particularly near the threshold where numerical errors could be larger. In the revised manuscript, we have added a dedicated subsection to §3 describing the convergence tests performed. We used three resolutions (with grid spacings differing by factors of 1.5) and demonstrate second-order convergence in the extracted spin and mass changes. Using Richardson extrapolation, we estimate the truncation error in the maximum spin-up to be less than 0.02 and in the mass gain less than 1%. These tests confirm that the reported values of 0.3 and 15% are robust within the stated uncertainties, and the linear trend holds across resolutions. revision: yes

  2. Referee: [§3] §3 (Numerical setup): The manuscript must document the grid resolutions employed, the location of outer boundaries, and any tests of initial-data gauge or constraint-violation effects. Without these, it is impossible to assess whether the reported spin and mass changes for the closest-to-threshold runs are free of systematic numerical artifacts.

    Authors: We acknowledge that the original §3 provided an overview of the numerical methods but lacked specific details on resolutions and boundaries. In the revision, we have expanded §3 to include: the base grid resolution of Δx = 0.025M in the finest level, with adaptive mesh refinement up to 8 levels; outer boundaries placed at 800M with outgoing wave boundary conditions; and results from constraint violation monitoring showing L2 norms below 10^{-5} throughout the evolution. Additionally, we tested sensitivity to initial data gauge choices and found variations in final χ and M of less than 3%, which is smaller than the reported effects. These additions should allow the reader to assess the absence of significant numerical artifacts. revision: yes

Circularity Check

0 steps flagged

No circularity: results are direct simulation outputs

full rationale

The paper reports quantitative findings (maximum spin-up 0.3, mass gain 15%, linear trend at threshold angle) obtained from a suite of numerical relativity simulations of equal-mass black-hole encounters. No analytical derivation chain, ansatz, or fitted-parameter prediction is presented that could reduce to its own inputs by construction. The central claims are extracted horizon quantities from the evolved spacetimes; they do not rely on self-definitional relations, load-bearing self-citations, or renaming of known results. The work is therefore self-contained as a computational survey.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

This is a purely numerical study. No free parameters are introduced or fitted; results emerge from solving the Einstein equations for specified initial data. Axioms are the standard assumptions of classical general relativity and the validity of the numerical scheme used.

axioms (1)
  • standard math Einstein's field equations govern the spacetime dynamics of the black hole encounter
    All simulations solve the vacuum Einstein equations numerically.

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Forward citations

Cited by 1 Pith paper

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

  1. Gravitational radiation from hyperbolic orbits: comparison between self-force, post-Minkowskian, post-Newtonian, and numerical relativity results

    gr-qc 2025-12 unverdicted novelty 5.0

    Self-force calculations of radiated gravitational wave energy from hyperbolic orbits around Schwarzschild black holes agree with post-Minkowskian results for large impact parameters and velocities up to 0.7c, with fur...

Reference graph

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