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On mass inflation and late-time divergences in limiting-curvature regular black holes

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Johanna Borissova

General Relativity and Quantum Cosmology · Submitted 3 Nov 2026 · 55 references

Pith's verdict: Competent extension of mass inflation analysis to a broader class of regular black holes; the core result is a condition that separates eternal exponential divergence from tamed power-law scaling, but the model's limitations are clearly acknowledged.

T0 · AI review

How this review was made: An AI referee (deepseek/deepseek-v4-flash) read the paper on November 4, 2026 and answered a fixed list of questions about it. T0 is the starting level every paper gets. The levels describe how deeply Pith has checked the paper, never the authors.

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arXiv ID2611.04618 (version 1)
Pith IDF34XTSNX, Pith's permanent record of this paper and its review
CitationJohanna Borissova. "On mass inflation and late-time divergences in limiting-curvature regular black holes." arXiv:2611.04618 (2026). https://pith.science/paper/F34XTSNX
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The paper

The paper claims

For a class of limiting-curvature regular black holes, the late-time divergence of the Misner-Sharp mass density forces an auxiliary mass parameter to become negative, imaginary, or complex, or requires a dynamical continuation of the…

The reading

This paper establishes that for static, spherically symmetric regular black holes with an $m$-independent upper bound on the Misner-Sharp mass density, the late-time behavior of mass inflation under perturbation is not necessarily exponential. Following a transient exponential phase, the Misner-Sharp mass density diverges as a fractional power law that can be made arbitrarily weak by tuning a parameter $n$ in the generalized Fan-Wang family. The key geometric insight is that this divergence forces an auxiliary 'unphysical' mass parameter $m_+(v)$ to evolve outside the positive-real numbers: for the Hayward black hole ($n=1$) it becomes negative; for $n=2$ it becomes purely imaginary; for $n>2$ it becomes complex. For certain generating functions, mass inflation remains eternal. The analysis is grounded in the generalized Ori model and the algebraic equation $h(\psi)=2m/r^3$ that defines the class.

What carries the argument

The central object is the generating function $h(\psi)$ satisfying $h(2M/r^3)=2m/r^3$, with a pole at $\psi_{\max}=1/\ell^2$ that encodes the limiting Misner-Sharp mass density. Its inverse $H(\varrho)$ maps the asymptotic mass to the metric. The generalized Ori model provides the dynamical equations for the shell radius $R(v)$ and the interior mass parameter $m_+(v)$, which at late times reduce to a Bernoulli differential equation for $\psi_+(v)$. The crucial diagnostic is the ratio $h(\psi)/h'(\psi)$: if it grows linearly for large $\psi$, mass inflation is eternal; otherwise, the late-time divergence is a power law whose exponent is controlled by $n$.

Extended reading notes

Core claim

The central claim is that for the quasi-topological class of regular black holes characterized by the algebraic equation $h(\psi)=2m/r^3$, where $h$ is invertible with a pole at $\psi_{\max}=1/\ell^2$, the asymptotic late-time divergence of the Misner-Sharp mass density $\psi_+(v)$ forces the unphysical mass parameter $m_+(v)$ to approach the quasi-fixed point $m_{+*}=(-1)^{-1/n}r_-^3/(2\ell^2)$. For the Hayward case ($n=1$) this is negative real; for the generalized Fan-Wang family ($n=2,3,\ldots$) it becomes imaginary or complex. Whenever the ratio $h(\psi)/h'(\psi)$ grows linearly with $\psi$ for large $\psi$, mass inflation is eternal. The derivation uses the generalized Ori model with a null thin shell and Price-law ingoing flux, reducing the late-time dynamics to a Bernoulli equation whose solution yields a $v^{-(\gamma+1)/n}$ power law for the Misner-Sharp mass density.

Load-bearing premise

The outgoing perturbation is modeled as a pressureless null thin shell, and the ingoing flux is assumed to follow Price's law with a power-law decay $\gamma\geq 11$, which may not capture the full continuous crossflow of perturbations, as the authors acknowledge.

Editorial extensions

If this is right

  • Mass inflation in regular black holes need not be exponential; it can be a mild power-law divergence tunable to arbitrarily weak growth by increasing the parameter $n$ of the generalized Fan-Wang family.
  • The unphysical mass parameter $m_+(v)$ necessarily becomes negative, imaginary, or complex at late times, which suggests that the effective description of the interior requires a real metric that may involve a dynamical continuation to a different branch of the static spacetime.
  • For generating functions where $h(\psi)/h'(\psi)\sim \psi$ for large $\psi$, mass inflation is eternal, indicating that not all limiting-curvature regular black holes avoid the late-time exponential instability.
  • The analysis provides a geometric criterion (the asymptotic form of $h$) to distinguish regular black holes that can tame mass inflation from those that cannot.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • If the late-time divergence is sufficiently weak (large $n$), the Cauchy horizon may be effectively stable on astrophysical timescales, making these regular black holes viable observational alternatives to singular black holes.
  • The appearance of a complex mass parameter in the generalized Ori model suggests that a full treatment in a quantum-gravity or higher-curvature theory, where $h$ arises from a resummation, may impose reality conditions that cap the growth at the limiting curvature.
  • The paper's formalism could be applied to test mass inflation in other regular black hole models, such as the Bardeen or Dymnikova metrics, to see if they belong to a class that tames or eternalizes the instability.
Original abstract

Mass inflation in non-extremal regular black holes with a non-linear dependence of the Misner-Sharp mass $M$ on the asymptotic mass $m>0$ may be a transient phenomenon followed by a model-dependent non-exponential late-time divergence. We analyse these regimes based on the generalised Ori model for a class of static spherically symmetric and asymptotically flat regular black holes with a de Sitter core and an $m$-independent upper bound on the Misner-Sharp mass density and Kretschmann scalar inspired by quasi-topological gravity. We discuss the geometric mechanism behind divergences of physical quantities at the inner horizon of the perturbed spacetime, and show that these require the unphysical mass parameter inside the shell to evolve outside the positive-real domain, or in some cases force a distinct type of dynamical continuation of the static metric. Imposing an asymptotic late-time divergence in form of a fractional power-law scaling, tunable to be arbitrarily mild within the considered approximation and effectively taming mass inflation, allows us to single out a family of generalised Fan-Wang regular black holes.

The compiled record

The paper's own sentences, arranged, kept beside the review and separate from it. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.

Compiled by classifier-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-11-04: 1 request, 3,978 input tokens.

What the abstract itself states, as probabilities: claims first 0.03 · states limitation 0.76 · human participants 0.01 · controlled comparison 0.03 · randomized assignment 0.01 · states quantitative result 0.18 · compares with prior results 0.30 · mentions code or data availability 0.02.

The abstract, sentence by sentence

arXiv listing abstract v1. Results and the main claim are underlined; .

Mass inflation in non-extremal regular black holes with a non-linear dependence of the Misner-Sharp mass $M$ on the asymptotic mass $m>0$ may be a transient phenomenon followed by a model-dependent non-exponential late-time divergence. We analyse these regimes based on the generalised Ori model for a class of static spherically symmetric and asymptotically flat regular black holes with a de Sitter core and an $m$-independent upper bound on the Misner-Sharp mass density and Kretschmann scalar inspired by quasi-topological gravity. We discuss the geometric mechanism behind divergences of physical quantities at the inner horizon of the perturbed spacetime, and show that these require the unphysical mass parameter inside the shell to evolve outside the positive-real domain, or in some cases force a distinct type of dynamical continuation of the static metric. Imposing an asymptotic late-time divergence in form of a fractional power-law scaling, tunable to be arbitrarily mild within the considered approximation and effectively taming mass inflation, allows us to single out a family of generalised Fan-Wang regular black holes.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#sentencerolethe authors' own workstates the main conclusionstrength
s0 Mass inflation in non-extremal regular black holes with a non-linear dependence of the Misner-Sharp mass $M$ on the asymptotic mass $m>0$ may be a transient phenomenon followed by a model-dependent non-exponential late-time divergence. result 0.62 0.19 0.51 hedged possibility 1.00
s1 We analyse these regimes based on the generalised Ori model for a class of static spherically symmetric and asymptotically flat regular black holes with a de Sitter core and an $m$-independent upper bound on the Misner-Sharp mass density and Kretschmann scalar inspired by quasi-topological gravity. method 0.82 0.93 0.07 asserted 0.97
s2 We discuss the geometric mechanism behind divergences of physical quantities at the inner horizon of the perturbed spacetime, and show that these require the unphysical mass parameter inside the shell to evolve outside the positive-real domain, or in some cases force a distinct type of dynamical continuation of the static metric. result 0.79 0.90 0.25 asserted 1.00
s3 Imposing an asymptotic late-time divergence in form of a fractional power-law scaling, tunable to be arbitrarily mild within the considered approximation and effectively taming mass inflation, allows us to single out a family of generalised Fan-Wang regular black holes. result 0.54 0.90 0.49 asserted 0.94

What kind of paper the classifier reports this is: theoretical result 1.00 · evidence from proof or derivation 0.99.

What was examined, and what was not

sources read
  • arXiv listing abstract v1
not examined
  • full text
  • figures and tables
  • references and citing sentences
  • relations to other papers
levels run
  • P abstract
not run
  • S sections
  • T body sentences
  • C citations
  • R cross-paper relations

Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

Figures
Figure 1. FIG. 1: Radial position of the shell
Figure 2. FIG. 2: Misner-Sharp mass
Figure 3. FIG. 3: Radial position of the shell
Figure 4. FIG. 4: Misner-Sharp mass
Figure 5. FIG. 5: Kretschmann scalar
Figure 6. FIG. 6: Kretschmann scalar
Figure 7. FIG. 7: Absolute value of the generating functions
Figure 8. FIG. 8: Misner-Sharp mass
Figure 9. FIG. 9: Radial position of the shell
Figure 10. FIG. 10: Misner-Sharp mass
Figure 11. FIG. 11: Radial position of the shell
Figure 12. FIG. 12: Misner-Sharp mass densities
Figure 13. FIG. 13: Misner-Sharp mass
Figure 14. FIG. 14: Radial position of the shell

Figures reproduced from arXiv:2611.04618 by the authors.

References

Discussion

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