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arxiv: 2606.24642 · v2 · pith:N5MXROZPnew · submitted 2026-06-23 · 🌀 gr-qc · hep-ph

When Black Holes Can Wear Pants

Giacomo Cacciapaglia , Manuel Del Piano , Francesco Sannino , Vania Vellucci This is my paper

Pith reviewed 2026-06-25 22:54 UTC · model grok-4.3

classification 🌀 gr-qc hep-ph
keywords black hole fragmentationpants topologyBekenstein-Hawking entropyGregory-Laflamme instabilitysuperradiancemodified gravityprimordial black holesKerr black holes
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The pith

Black hole fragmentation into multiple horizons is forbidden by the area law and kinematics in classical four-dimensional general relativity but can become entropically favored in higher dimensions, under superradiance, or in modified gravi

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

The paper maps the conditions under which a black hole horizon can split into two or more smaller horizons, producing a pants-like topology. In standard general relativity the Bekenstein-Hawking area law rules out fragmentation for Schwarzschild black holes while spin and conservation laws add further barriers for Kerr black holes, with only a possible loophole near extremality. The authors examine three classes of extension where entropy can increase upon emitting small fragments: the Gregory-Laflamme instability in higher dimensions, superradiant trapping of radiation, and four-dimensional models that alter the entropy-mass or radius-mass relation. In each case fragmentation remains possible only when the initial kinematic configuration permits it. The analysis bears on primordial black holes and on the final state after mergers.

Core claim

In classical general relativity the Bekenstein-Hawking area law forbids black hole fragmentation for Schwarzschild black holes, and kinematic constraints prevent it for Kerr black holes except possibly near-extremal cases; fragmentation can be entropically favored in higher-dimensional, superradiant, or modified-gravity scenarios but still depends on initial kinematics.

What carries the argument

black hole fragmentation, the splitting of one horizon into multiple horizons whose total area and entropy are compared against the initial state

If this is right

  • Emission of small fragments can increase total entropy when the entropy-mass relation is altered by extra dimensions or modified gravity.
  • Kinematic constraints still limit which initial black hole states can actually fragment even when entropy favors the process.
  • Primordial black holes in higher-dimensional or modified-gravity cosmologies could evolve by shedding smaller black holes.
  • Black hole mergers could end with multiple remnants instead of a single final black hole if the post-merger state satisfies the fragmentation conditions.

Where Pith is reading between the lines

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

  • Gravitational-wave signals from mergers might carry signatures of temporary multi-horizon states if fragmentation occurs.
  • The same entropy-versus-kinematics logic could be applied to test specific modified-gravity models against future black-hole observations.
  • Near-extremal astrophysical black holes become the most interesting targets for searching fragmentation effects.

Load-bearing premise

Entropic favorability or the presence of an instability is sufficient to overcome kinematic barriers and produce actual fragmentation rather than merely permitting it in principle.

What would settle it

A numerical simulation of a near-extremal Kerr black hole or a higher-dimensional black hole that shows an instability causing the horizon to split into two separate horizons within finite time.

Figures

Figures reproduced from arXiv: 2606.24642 by Francesco Sannino, Giacomo Cacciapaglia, Manuel Del Piano, Vania Vellucci.

Figure 1
Figure 1. Figure 1: FIG. 1. Simplest diagram representing black hole pants: a single black hole of mass [PITH_FULL_IMAGE:figures/full_fig_p004_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. Regions in the parameter space of the two non-rotating fragments for four representative [PITH_FULL_IMAGE:figures/full_fig_p010_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. Regions in the parameter space [PITH_FULL_IMAGE:figures/full_fig_p013_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. Fragmentation of an ultra-spinning black hole of mass [PITH_FULL_IMAGE:figures/full_fig_p015_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5. Embedding of [PITH_FULL_IMAGE:figures/full_fig_p017_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6. Change of entropy in the fragmentation of a black hole of initial mass [PITH_FULL_IMAGE:figures/full_fig_p023_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: FIG. 7. The largest allowed mass fraction of the smaller fragment is shown in blue, while the red [PITH_FULL_IMAGE:figures/full_fig_p025_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: FIG. 8. Region favorable to fragmentation, with increase in entropy in Eq. [PITH_FULL_IMAGE:figures/full_fig_p028_8.png] view at source ↗
read the original abstract

We investigate the conditions under which black hole fragmentation, the splitting of a black hole horizon into multiple smaller ones, may occur. The simplest realization is that of a single black hole horizon splitting into two, giving rise to the eponymous pants topology. In classical general relativity, the Bekenstein-Hawking area law forbids such processes for Schwarzschild black holes. For spinning Kerr black holes, purely kinematic analyses impose constraints that prevent fragmentation, even in regimes where entropy considerations might allow it, except possibly in near-extremal cases. We then hunt for scenarios where black holes can wear pants: from the well-known Gregory-Laflamme instability in higher dimensions, to the potential effect of superradiant instabilities in non-axisymmetric radiation trapping, to finally gravitational models that modify the relations between entropy and/or horizon radius and the black hole mass in four dimensions. In all such cases, emission of small fragments can be entropically favored, however its occurrence still depends on the kinematic configuration of the initial state. Our analysis clarifies the theoretical landscape where black holes may fragment, which is particularly relevant for primordial black holes and catastrophic events such as black hole mergers.

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

0 major / 1 minor

Summary. The manuscript investigates conditions under which black hole fragmentation (splitting of a horizon into multiple smaller ones, yielding pants topology) may occur. It states that the Bekenstein-Hawking area law forbids fragmentation for Schwarzschild black holes in classical GR, while kinematic constraints prevent it for Kerr black holes except possibly near-extremal cases. The paper then examines scenarios where small-fragment emission can be entropically favored, including the Gregory-Laflamme instability in higher dimensions, superradiant instabilities, and modified-gravity models altering entropy-mass or horizon-radius relations in four dimensions. In all such cases, actual occurrence still depends on the kinematic configuration of the initial state. The analysis is framed as clarifying the theoretical landscape, with relevance to primordial black holes and mergers.

Significance. If the analysis holds, the work provides a useful map of the regimes where fragmentation is classically forbidden versus those where it becomes entropically allowed, while correctly emphasizing that entropic favorability alone does not guarantee dynamical realization. The explicit hedging regarding kinematic dependence is a strength that keeps the claims proportionate. No machine-checked proofs or reproducible code are mentioned, but the grounding in standard GR tools (area law, superradiance, Gregory-Laflamme) and the focus on falsifiable kinematic conditions add value to the literature on black-hole instabilities and modified gravity.

minor comments (1)
  1. [Abstract] The abstract refers to 'non-axisymmetric radiation trapping' without a brief parenthetical definition or reference; a short clarification would aid readers unfamiliar with the specific superradiant mechanism.

Simulated Author's Rebuttal

0 responses · 0 unresolved

We thank the referee for their positive assessment of the manuscript, including the recognition that the analysis provides a useful map of regimes where fragmentation is forbidden versus entropically allowed, while correctly emphasizing kinematic dependence. We are pleased that the referee recommends acceptance.

Circularity Check

0 steps flagged

No significant circularity

full rationale

The paper presents an analysis of black hole fragmentation conditions based on the standard Bekenstein-Hawking area law, kinematic constraints in GR, and known instabilities or modifications in other scenarios. No equations, derivations, or claims reduce by construction to fitted inputs, self-definitions, or self-citation chains. The central statements remain hedged on kinematic dependence and cite external established results without load-bearing self-references or renaming of known patterns as new derivations. The derivation chain is self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Abstract-only; no free parameters, axioms, or invented entities can be identified from the provided text.

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    GENERAL RELATIVITY CONSTRAINTS ON BLACK HOLE PANTS, A BRIEF SUMMARY We will first critically analyze why common lore says that black hole fragmentation is forbidden in GR by the second law of black hole thermodynamics. This law has a crucial assumption: the absence of matter violating the Null Energy Condition. This condition, however, is invalidated in m...

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