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arxiv: 2509.20450 · v3 · submitted 2025-09-24 · 🌀 gr-qc · astro-ph.HE· hep-th

Splitting the Gravitational Atom: Instabilities of Black Holes with Synchronized or Resonant Hair

Jordan Nicoules , Jos\'e Ferreira , Carlos A. R. Herdeiro , Eugen Radu , Miguel Zilh\~ao This is my paper

Pith reviewed 2026-05-18 13:44 UTC · model grok-4.3

classification 🌀 gr-qc astro-ph.HEhep-th
keywords black holesbosonic hairsuperradianceinstabilitiesnumerical relativitysynchronized hairresonant hair
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The pith

Black holes with synchronized bosonic hair eject their horizons from the scalar cloud in the very hairy regime.

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

This paper studies black holes carrying synchronized bosonic hair that arise from superradiance of ultralight fields and connect to bosonic stars. In the very hairy regime, where a small horizon sits inside a scalar cloud that holds most of the energy, numerical evolutions show the horizon being pushed out of the cloud's center. A similar ejection appears in a related family of black holes with resonant scalar hair, although the final state differs. The authors argue this splitting is probably generic for sufficiently hairy solutions across the broader class of synchronized and resonant hair models.

Core claim

For black holes with synchronized bosonic hair in the very hairy regime, the horizon gets naturally ejected from the center of its scalar environment, and a similar dynamics occurs in black holes with resonant scalar hair albeit with a different fate.

What carries the argument

The very hairy regime of synchronized or resonant bosonic hair, in which a small black hole horizon sits inside a dominant scalar cloud and undergoes dynamical ejection.

Load-bearing premise

The initial data accurately represent genuine equilibrium solutions in the very hairy regime and the subsequent evolution contains no numerical artifacts that artificially produce the observed ejection.

What would settle it

A long-duration numerical evolution starting from a slightly perturbed very hairy synchronized-hair solution in which the horizon remains centered without ejection would falsify the instability.

Figures

Figures reproduced from arXiv: 2509.20450 by Carlos A. R. Herdeiro, Eugen Radu, Jordan Nicoules, Jos\'e Ferreira, Miguel Zilh\~ao.

Figure 1
Figure 1. Figure 1: FIG. 1. (Left) BHsSH in the simplest scalar model: a horizon inside [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. The BHSH configuration [PITH_FULL_IMAGE:figures/full_fig_p002_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. Mass transfer between the BH and scalar field. The most [PITH_FULL_IMAGE:figures/full_fig_p003_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. Fraction of scalar energy (main panel) and total spacetime [PITH_FULL_IMAGE:figures/full_fig_p003_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5. Snapshots of the density of the scalar field in the [PITH_FULL_IMAGE:figures/full_fig_p004_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6. Angular momentum transfer between the BH and scalar field. [PITH_FULL_IMAGE:figures/full_fig_p006_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: FIG. 7. Evolution of the BH dimensionless spin. [PITH_FULL_IMAGE:figures/full_fig_p006_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: FIG. 8. Second-order convergence of the matter energy [PITH_FULL_IMAGE:figures/full_fig_p008_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: FIG. 9. Convergence to zero of the norm-2 of the Hamiltonian constraint [PITH_FULL_IMAGE:figures/full_fig_p008_9.png] view at source ↗
read the original abstract

Black holes (BHs) with synchronized bosonic hair challenge the Kerr paradigm, linking superradiance from ultralight fields -- creating gravitational atoms -- to bosonic stars across parameter space. In the ''very hairy'' regime, where a small horizon lies inside a bosonic star containing most of the energy, they deviate sharply from Kerr, but their dynamics remain unexplored. We show that for such solutions the horizon gets naturally ejected from the center of its scalar environment, and observe a similar dynamics in a cousin model of BHs with resonant scalar hair, albeit with a different fate. This dynamical splitting is likely to be generic for sufficiently hairy BHs in the broader class of models with synchronized or resonant hair, but possible exceptions may exist.

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 / 0 minor

Summary. The paper numerically investigates the nonlinear dynamics of black holes with synchronized bosonic hair in the very hairy regime, where a small horizon sits inside a dominant bosonic star. Using 3+1 evolutions of the Einstein-Klein-Gordon system, it reports that the horizon is ejected from the center of the scalar environment. An analogous ejection is found in a resonant-hair cousin model, albeit with a different final state. The authors conclude that such splitting is likely generic for sufficiently hairy solutions in this broader class.

Significance. If the reported ejection is physical, the result would be significant: it supplies the first direct evidence that very-hairy synchronized and resonant solutions are dynamically unstable, thereby linking stationary hairy black holes to their likely end-states and sharpening the connection between superradiance, bosonic stars, and the Kerr paradigm. The numerical approach yields concrete, falsifiable predictions for the timescale and morphology of the splitting.

major comments (1)
  1. Numerical Methods / Results sections: The central claim that the horizon is 'naturally ejected' rests on time evolutions of very-hairy initial data, yet no convergence tests with resolution, no histories of constraint violations, and no explicit verification that the initial time derivatives vanish to machine precision are presented. Without these diagnostics it remains possible that truncation or gauge errors seed the observed radial motion, undermining the physical interpretation of the instability.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for their careful reading of the manuscript and for highlighting the importance of numerical diagnostics. We address the major comment below and will incorporate the requested material in the revised version.

read point-by-point responses

  1. Referee: [—] Numerical Methods / Results sections: The central claim that the horizon is 'naturally ejected' rests on time evolutions of very-hairy initial data, yet no convergence tests with resolution, no histories of constraint violations, and no explicit verification that the initial time derivatives vanish to machine precision are presented. Without these diagnostics it remains possible that truncation or gauge errors seed the observed radial motion, undermining the physical interpretation of the instability.

    Authors: We agree that the original manuscript did not present explicit convergence tests, constraint-violation histories, or a direct verification that the initial time derivatives vanish to machine precision. These omissions leave open the possibility that numerical artifacts could influence the reported dynamics. In the revised manuscript we will add (i) a convergence study at three resolutions demonstrating that the ejection timescale and morphology converge, (ii) time histories of the Hamiltonian and momentum constraint violations showing they remain small and do not grow secularly, and (iii) a quantitative check that the initial data satisfy the stationary equations to machine precision with vanishing time derivatives. These additions will confirm that the observed splitting is not seeded by truncation or gauge errors. revision: yes

Circularity Check

0 steps flagged

No circularity: result follows from direct numerical evolution of the Einstein-Klein-Gordon system

full rationale

The paper constructs stationary initial data for synchronized or resonant hairy black holes by solving the elliptic Einstein-scalar equations in the very-hairy regime, then evolves these data forward using 3+1 numerical relativity. The reported horizon ejection emerges from the time-dependent dynamics and is not presupposed by the initial-data construction or by any fitted parameter. No equation or claim reduces the instability to a self-definition, a renamed input, or a load-bearing self-citation whose validity is assumed rather than independently verified. The derivation chain is therefore self-contained against the underlying field equations.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The work assumes the validity of classical general relativity coupled to a massive scalar field and the existence of equilibrium hairy black hole solutions obtained in earlier papers; no new free parameters or invented entities are introduced in the abstract.

axioms (1)
  • standard math The Einstein-Klein-Gordon system governs the spacetime and scalar field evolution
    Standard field equations of general relativity with a complex scalar field, invoked implicitly for the time evolution.

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Forward citations

Cited by 3 Pith papers

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

  1. Spontaneous spherical symmetry breaking of black holes with resonant hair

    gr-qc 2026-04 unverdicted novelty 5.0

    Black holes with resonant hair spontaneously break spherical symmetry and decay into bald black holes via non-spherical dynamics, either through fission or absorption.

  2. Black Hole-Boson Star Binaries: Gravitational Wave Signals and Tidal Disruption

    gr-qc 2026-04 unverdicted novelty 5.0

    Numerical simulations of black hole-boson star binaries show that scalar self-interactions can suppress tidal disruption while radiative efficiency depends on the chosen potential.

  3. Gravitational Atoms from Topological Stars

    gr-qc 2025-11 unverdicted novelty 5.0

    Bound states of a massive scalar field around topological stars form strictly normal modes, producing a hydrogen-like spectrum when the Compton wavelength exceeds the star size and localized states otherwise.

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