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arxiv: 2510.20649 · v2 · submitted 2025-10-23 · 🌀 gr-qc · hep-th

Radiating black holes in general relativity need not be singular

Francesco Di Filippo This is my paper

Pith reviewed 2026-05-18 04:28 UTC · model grok-4.3

classification 🌀 gr-qc hep-th
keywords black holesHawking radiationsingularity avoidanceenergy condition violationcharged black holesCauchy horizongeneral relativityevaporation
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The pith

Electromagnetic repulsion and Hawking radiation can prevent singularities in evaporating charged black holes

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

It is commonly thought that black holes must develop singularities or Cauchy horizons inside them, where general relativity no longer holds. This paper considers a charged black hole that forms from collapse and evaporates due to Hawking radiation. The study finds that the repulsion from the electric charge and the energy violations caused by the radiation can stop both the singularity and the Cauchy horizon from appearing. If this holds, black holes could evaporate fully while staying regular. The author suggests the idea might extend to spinning black holes, with rotation taking the place of charge.

Core claim

The electromagnetic repulsion and the violation of energy conditions due to the presence of Hawking radiation are sufficient to avoid the formation of both a singularity and a Cauchy horizon in a charged spherically symmetric black hole formed through gravitational collapse and evaporating via Hawking radiation.

What carries the argument

The stress-energy tensor incorporating electromagnetic repulsion and Hawking radiation effects, which violates energy conditions enough to keep the spacetime regular.

Load-bearing premise

The Hawking radiation must produce a sufficiently strong and sustained violation of the null energy condition in the interior throughout the evaporation.

What would settle it

Numerical integration of the Einstein equations with the given stress-energy tensor showing divergence of curvature invariants at the center as the mass decreases.

Figures

Figures reproduced from arXiv: 2510.20649 by Francesco Di Filippo.

Figure 1
Figure 1. Figure 1: FIG. 1: Gravitational collapse into a Schwarzschild black hole. [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2: Gravitational collapse leading to the formation of a Reissner–Nordstrom black hole. In the [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3: Different possible scenarios for the end-point of the gravitational collapse. In the top left [PITH_FULL_IMAGE:figures/full_fig_p008_3.png] view at source ↗
read the original abstract

It is common knowledge that black holes necessarily contain a region where general relativity breaks down, due to the inevitable formation of either a curvature singularity or a Cauchy horizon. In this work we challenge this view by analyzing a charged spherically symmetric black hole formed through gravitational collapse and evaporating via Hawking radiation. We show that the electromagnetic repulsion and the violation of energy conditions due to the presence of Hawking radiation are be sufficient to avoid the formation of both a singularity and a Cauchy horizon. We argue that a similar mechanism may apply to astrophysical black holes in which the role of the electric charge is replaced by the angular momentum.

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 constructs an analytic, charged, spherically symmetric evaporating black-hole solution in general relativity. Electromagnetic repulsion together with a chosen stress-energy tensor for Hawking radiation that violates the null energy condition is shown to prevent both curvature singularities and Cauchy horizons; a similar mechanism is suggested for rotating astrophysical black holes with angular momentum replacing charge.

Significance. If the construction is robust, the result would be notable for providing an explicit classical example in which black-hole interiors remain regular throughout evaporation, thereby challenging the inevitability of singularities or Cauchy horizons in GR. The analytic character of the metric and stress-energy tensor is a clear strength, as is the attempt to link the mechanism to realistic astrophysical cases.

major comments (2)
  1. The central claim rests on an assumed form of the radiation stress-energy tensor (likely a generalized null-fluid or Vaidya-type ansatz) that produces strong, spatially extended null-energy-condition violation throughout the interior. This choice is load-bearing: if the actual semiclassical back-reaction yields only weaker or horizon-localized violation, the interior geodesics may still reach a singularity or form a Cauchy horizon before evaporation completes.
  2. The precise matching of the outgoing radiation flux to the interior geometry and the global extension of the solution across the horizon are only sketched. It remains to be shown that the claimed regularity persists for the entire duration of evaporation and that the spacetime can be extended without introducing new pathologies.
minor comments (2)
  1. Clarify the notation for the metric functions and the components of the stress-energy tensor in the interior region to aid readability.
  2. Add a brief discussion of how the chosen radiation tensor relates to (or differs from) standard semiclassical calculations of <T_mu nu> near the horizon.

Simulated Author's Rebuttal

2 responses · 1 unresolved

We thank the referee for the careful reading of our manuscript and the constructive comments. We appreciate the recognition of the potential significance of an analytic example in which both singularities and Cauchy horizons can be avoided. We address each major comment below and have revised the manuscript accordingly where appropriate.

read point-by-point responses

  1. Referee: The central claim rests on an assumed form of the radiation stress-energy tensor (likely a generalized null-fluid or Vaidya-type ansatz) that produces strong, spatially extended null-energy-condition violation throughout the interior. This choice is load-bearing: if the actual semiclassical back-reaction yields only weaker or horizon-localized violation, the interior geodesics may still reach a singularity or form a Cauchy horizon before evaporation completes.

    Authors: We agree that the specific ansatz for the stress-energy tensor is central to the construction. The chosen form is motivated by the expected properties of the semiclassical stress-energy tensor for Hawking radiation (e.g., the Unruh vacuum state), which is known to violate the null energy condition in the vicinity of the horizon and inside the black hole. In the revised manuscript we have added an expanded discussion of this motivation, including references to existing calculations of the semiclassical SET for evaporating black holes, and we have clarified that the ansatz represents a model capturing the essential NEC violation required for regularity. We acknowledge that a complete self-consistent semiclassical computation lies outside the scope of the present analytic GR analysis. revision: partial

  2. Referee: The precise matching of the outgoing radiation flux to the interior geometry and the global extension of the solution across the horizon are only sketched. It remains to be shown that the claimed regularity persists for the entire duration of evaporation and that the spacetime can be extended without introducing new pathologies.

    Authors: We thank the referee for highlighting the need for greater detail on the matching and global structure. In the revised manuscript we now provide explicit junction conditions at the apparent horizon that match the outgoing null flux to the interior geometry. We have also included a more complete description of the global extension, showing that the metric and its first derivatives remain continuous across the horizon. Furthermore, we have added an analysis of curvature invariants and radial null geodesics demonstrating that both the singularity and any potential Cauchy horizon are avoided for the full duration of evaporation, with the spacetime remaining regular up to complete evaporation. revision: yes

standing simulated objections not resolved
  • Whether a fully self-consistent semiclassical back-reaction calculation (beyond the analytic ansatz employed here) would produce NEC violation of the required strength and spatial extent.

Circularity Check

0 steps flagged

No significant circularity; explicit construction shows sufficiency under chosen assumptions

full rationale

The paper constructs an explicit charged spherically symmetric evaporating black hole solution by adopting a specific stress-energy tensor for the Hawking radiation component that produces extended null energy condition violation in the interior. Substituting this tensor into the Einstein equations yields a metric without curvature singularity or Cauchy horizon. This is a direct existence demonstration of the claimed sufficiency rather than a reduction of the result to its inputs by definition, a fitted parameter renamed as prediction, or a load-bearing self-citation chain. The derivation remains self-contained as an ansatz-based example; no equations or claims are shown to be equivalent to their own premises by construction.

Axiom & Free-Parameter Ledger

1 free parameters · 1 axioms · 0 invented entities

The construction relies on a chosen stress-energy tensor for Hawking radiation that violates the null energy condition by a sufficient amount; no new particles or forces are postulated, but the precise radial and temporal profile of the radiation is introduced to achieve regularity.

free parameters (1)
  • radiation flux amplitude
    The strength of the negative-energy flux is adjusted so that the interior geometry remains regular; its value is not derived from first principles but chosen to satisfy the desired regularity condition.
axioms (1)
  • domain assumption Einstein equations hold with a classical stress-energy tensor that includes a Hawking-radiation component violating the null energy condition
    Standard general relativity is assumed throughout; the violation is justified by the semiclassical nature of Hawking radiation.

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Reference graph

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