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arxiv: 2606.30865 · v1 · pith:6IIBRJKInew · submitted 2026-06-29 · 🌀 gr-qc · astro-ph.HE· hep-th

Scalarization and descalarization in hyperbolic encounters of black holes

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

Pith reviewed 2026-07-01 01:19 UTC · model grok-4.3

classification 🌀 gr-qc astro-ph.HEhep-th
keywords scalarizationblack holesGauss-Bonnethyperbolic encountersnumerical relativitydynamical effectsspin changes
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The pith

Black holes in hyperbolic encounters temporarily scalarize even when their static parameters forbid scalar hair, and spin changes can make it permanent.

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

This paper investigates scalar field behavior during close flybys of black holes in a modified theory of gravity. It finds that encounters can induce temporary scalar hair on black holes that would not support it individually. Spin alterations from the interaction can also cause lasting scalarization or the loss of it. These results highlight how binary dynamics can trigger scalar effects beyond what isolated black holes allow.

Core claim

Configurations which initially cannot sustain a scalar hair temporarily scalarize during an encounter and thereby exhibit dynamical scalarization. The change in the spin magnitude of black holes during certain hyperbolic encounters can lead to permanent spin-induced scalarization (or descalarization). This occurs in the decoupling limit for both positive and negative couplings with zero and non-zero spins.

What carries the argument

Evolution of the scalar field on a fixed background metric of the black hole binary in quadratic scalar Gauss-Bonnet gravity.

Load-bearing premise

The scalar field does not back-react on the spacetime geometry.

What would settle it

A calculation or simulation that includes the scalar field's effect on the metric and shows the absence of dynamical scalarization in the same setups would falsify the decoupling-limit results.

Figures

Figures reproduced from arXiv: 2606.30865 by Frederick C.L. Pardoe, Helvi Witek.

Figure 1
Figure 1. Figure 1: FIG. 1. Diagram illustrating the initial setup of the GR [PITH_FULL_IMAGE:figures/full_fig_p006_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. The change in spin, [PITH_FULL_IMAGE:figures/full_fig_p007_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. Schematic depiction of the phenomenology of close encounters in quadratic sGB gravity. Time moves from left to right. [PITH_FULL_IMAGE:figures/full_fig_p008_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. Snapshots of the scalar field, [PITH_FULL_IMAGE:figures/full_fig_p011_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5. Multipoles of the scalar field, [PITH_FULL_IMAGE:figures/full_fig_p011_5.png] view at source ↗
Figure 7
Figure 7. Figure 7: FIG. 7. The scalar field, [PITH_FULL_IMAGE:figures/full_fig_p012_7.png] view at source ↗
Figure 9
Figure 9. Figure 9: FIG. 9. Multipoles of the scalar field, [PITH_FULL_IMAGE:figures/full_fig_p013_9.png] view at source ↗
Figure 8
Figure 8. Figure 8: FIG. 8. Snapshots of the scalar field, [PITH_FULL_IMAGE:figures/full_fig_p013_8.png] view at source ↗
Figure 11
Figure 11. Figure 11: FIG. 11. Multipoles of the scalar field, [PITH_FULL_IMAGE:figures/full_fig_p014_11.png] view at source ↗
Figure 10
Figure 10. Figure 10: FIG. 10. Snapshots of the scalar field, [PITH_FULL_IMAGE:figures/full_fig_p014_10.png] view at source ↗
Figure 12
Figure 12. Figure 12: FIG. 12. Snapshots of the scalar field, [PITH_FULL_IMAGE:figures/full_fig_p015_12.png] view at source ↗
Figure 13
Figure 13. Figure 13: FIG. 13. Multipoles of the scalar field, [PITH_FULL_IMAGE:figures/full_fig_p016_13.png] view at source ↗
Figure 14
Figure 14. Figure 14: FIG. 14. The scalar field, [PITH_FULL_IMAGE:figures/full_fig_p017_14.png] view at source ↗
Figure 15
Figure 15. Figure 15: FIG. 15. Snapshots of the scalar field, [PITH_FULL_IMAGE:figures/full_fig_p018_15.png] view at source ↗
Figure 17
Figure 17. Figure 17: FIG. 17. Profile of the scalar field, [PITH_FULL_IMAGE:figures/full_fig_p019_17.png] view at source ↗
Figure 18
Figure 18. Figure 18: FIG. 18. Snapshots of the scalar field, [PITH_FULL_IMAGE:figures/full_fig_p020_18.png] view at source ↗
Figure 19
Figure 19. Figure 19: FIG. 19. Top panel: Multipoles of the scalar field, [PITH_FULL_IMAGE:figures/full_fig_p021_19.png] view at source ↗
Figure 21
Figure 21. Figure 21: FIG. 21. Convergence plot of the scalar charge in the Ex [PITH_FULL_IMAGE:figures/full_fig_p024_21.png] view at source ↗
Figure 23
Figure 23. Figure 23: FIG. 23. Convergence plot of the scalar field in the [PITH_FULL_IMAGE:figures/full_fig_p024_23.png] view at source ↗
Figure 24
Figure 24. Figure 24: FIG. 24. Convergence plot of the scalar field in the Ex [PITH_FULL_IMAGE:figures/full_fig_p025_24.png] view at source ↗
read the original abstract

We use numerical relativity to study the scalar field evolution sourced by hyperbolic encounters of black holes in quadratic scalar Gauss-Bonnet gravity. In this theory, single black holes are known to acquire a scalar hair through scalarization for certain values of their mass and spin. We work in the decoupling limit and evolve the scalar field on top of a background metric. Seeding binary black holes with an initial scalar field, we find that configurations which initially cannot sustain a scalar hair temporarily scalarize during an encounter and thereby exhibit dynamical scalarization. This is possible for both positive and negative couplings between the scalar field and curvature in black hole binaries with zero and non-zero initial spins, respectively. Furthermore, we find that the change in the spin magnitude of black holes during certain hyperbolic encounters can lead to permanent spin-induced scalarization (or descalarization), which we refer to as spin-up (de)scalarization.

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 / 1 minor

Summary. The paper uses numerical relativity simulations in the decoupling limit to evolve a scalar field on a fixed binary black hole background in quadratic scalar-Gauss-Bonnet gravity. It reports that black hole configurations initially unable to sustain scalar hair can temporarily scalarize during hyperbolic encounters (dynamical scalarization) for both positive and negative couplings, and that spin changes during the encounter can induce permanent spin-induced scalarization or descalarization.

Significance. If the decoupling limit remains valid, the results identify new dynamical channels for scalar hair formation and loss in black hole encounters, extending scalarization phenomenology beyond isolated or orbiting black holes. This could inform strong-field tests of modified gravity and potential gravitational-wave signatures from close encounters.

major comments (1)
  1. [Abstract and decoupling-limit setup] The decoupling limit (invoked to evolve the scalar on a fixed metric without backreaction) is load-bearing for both the dynamical scalarization and spin-induced (de)scalarization claims. When the scalar reaches O(1) amplitudes, the neglected scalar stress-energy could alter curvature invariants, orbital dynamics, and final spins, potentially shifting or eliminating the reported thresholds. The manuscript should supply quantitative estimates of backreaction (e.g., via the magnitude of the scalar stress-energy relative to the background curvature) or convergence tests against the full Einstein-scalar system in representative regimes.
minor comments (1)
  1. [Abstract] The abstract summarizes the central numerical findings but omits any mention of error bars, resolution studies, or validation against known single-BH scalarization thresholds; adding a brief statement on these would strengthen the presentation.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for the positive assessment of the significance of our results and for the detailed major comment on the decoupling limit. We address the comment below.

read point-by-point responses

  1. Referee: [Abstract and decoupling-limit setup] The decoupling limit (invoked to evolve the scalar on a fixed metric without backreaction) is load-bearing for both the dynamical scalarization and spin-induced (de)scalarization claims. When the scalar reaches O(1) amplitudes, the neglected scalar stress-energy could alter curvature invariants, orbital dynamics, and final spins, potentially shifting or eliminating the reported thresholds. The manuscript should supply quantitative estimates of backreaction (e.g., via the magnitude of the scalar stress-energy relative to the background curvature) or convergence tests against the full Einstein-scalar system in representative regimes.

    Authors: We agree that the decoupling limit is a central approximation whose validity must be assessed, especially when scalar amplitudes reach O(1). In the revised manuscript we will add a dedicated discussion that supplies quantitative estimates of backreaction. These will consist of direct comparisons between the magnitude of the scalar stress-energy tensor and the background curvature invariants (Ricci scalar and Gauss-Bonnet invariant) evaluated at the times and locations of peak scalarization for representative encounters. This will allow readers to judge the regimes in which the reported dynamical and spin-induced (de)scalarization channels are expected to survive in the fully coupled theory. We note that full convergence tests against the coupled Einstein-scalar system lie outside the present scope, as they would require an entirely different numerical infrastructure. revision: yes

Circularity Check

0 steps flagged

No circularity: numerical evolution outputs independent of inputs

full rationale

The paper reports outcomes of numerical relativity simulations evolving a scalar field on a fixed binary black hole background in the decoupling limit. No equations reduce a claimed prediction to a fitted parameter or self-definition by construction. No load-bearing self-citations, uniqueness theorems, or ansatzes imported from prior author work are quoted. Results are framed as simulation findings rather than renamings or statistical forcings, satisfying the criteria for a self-contained derivation chain.

Axiom & Free-Parameter Ledger

2 free parameters · 1 axioms · 0 invented entities

The central claim rests on the decoupling limit and on the existence of scalarization thresholds for isolated black holes that are taken from prior literature.

free parameters (2)
  • scalar-curvature coupling strength
    Sign and magnitude control whether scalarization occurs; values are chosen to place systems inside or outside the scalarization regime.
  • initial black hole masses and spins
    Parameters selected so that isolated black holes lie outside the scalarization window before the encounter.
axioms (1)
  • domain assumption Decoupling limit: scalar field evolved on fixed background metric
    Stated explicitly in the abstract to justify the numerical setup.

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discussion (0)

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Reference graph

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