Integrable singularities obstruct Cauchy horizons and mass inflation

Abstract

Black-hole interiors with an inner (Cauchy) horizon are unstable through the Poisson-Israel-Ori mass-inflation mechanism, governed by the Dray-'t Hooft-Redmount relation and widely regarded as a dynamical realization of strong cosmic censorship. We show that static, spherically symmetric anisotropic interiors supported by a marginally divergent but integrable density ρ∼ A/r², with A>1/(8π) and mild screening at finite radius, are incompatible with this mechanism. The compactness q=m/r decreases monotonically from a super-critical central value to 1/2 at the unique event horizon, producing a strictly positive compactness gap throughout the trapped region and excluding any second zero of the lapse. This gap enters the dynamics quantitatively. (i) Under the null energy condition and a dynamical screening condition, 2m/r is non-decreasing along both future null directions of a trapped domain, so the gap propagates under nonlinear spherically symmetric evolution. (ii) For ingoing radiation (generalized Vaidya), the gap bounds the blueshift: the advanced time spent in the gapped region is finite, whereas it diverges at a Cauchy horizon. (iii) For counter-streaming null dust, the radiative part μ of the Misner-Sharp mass obeys exactly ∂_u∂_vμ=2 ∂_uμ ∂_vμ/(r|f|), of which the DTR relation is the thin-shell form; the in-out coupling 2/(r|f|) is uniformly bounded on the interior precisely when the gap is positive. This yields an a priori mass bound and, in the Ori thin-shell model, an e-folding rate bounded by the influx luminosity instead of tending to the inner-horizon surface gravity. Integrable-singularity interiors thus realize a class of sources for which the Poisson-Israel-Ori amplification channel is structurally inoperative in the models in which mass inflation was originally established.

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Cite

BibTeX RIS

BibTeX

@misc{telloortiz2026integrable,
  title = {{Integrable singularities obstruct Cauchy horizons and mass inflation}},
  author = {Francisco Tello-Ortiz},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.38826},
  eprint = {2610.38826},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.38826},
  note = {CC BY 4.0},
}

RIS

TY  - UNPB
TI  - Integrable singularities obstruct Cauchy horizons and mass inflation
AU  - Francisco Tello-Ortiz
PY  - 2026
DA  - 2026/10/28
PB  - arXiv
DO  - 10.48550/arxiv.2610.38826
UR  - https://arxiv.org/abs/2610.38826
AB  - Black-hole interiors with an inner (Cauchy) horizon are unstable through the Poisson-Israel-Ori mass-inflation mechanism, governed by the Dray-'t Hooft-Redmount relation and widely regarded as a dynamical realization of strong cosmic censorship. We show that static, spherically symmetric anisotropic interiors supported by a marginally divergent but integrable density ρ∼ A/r^2, with A>1/(8π) and mild screening at finite radius, are incompatible with this mechanism. The compactness q=m/r decreases monotonically from a super-critical central value to 1/2 at the unique event horizon, producing a strictly positive compactness gap throughout the trapped region and excluding any second zero of the lapse. This gap enters the dynamics quantitatively. (i) Under the null energy condition and a dynamical screening condition, 2m/r is non-decreasing along both future null directions of a trapped domain, so the gap propagates under nonlinear spherically symmetric evolution. (ii) For ingoing radiation (generalized Vaidya), the gap bounds the blueshift: the advanced time spent in the gapped region is finite, whereas it diverges at a Cauchy horizon. (iii) For counter-streaming null dust, the radiative part μ of the Misner-Sharp mass obeys exactly ∂_u∂_vμ=2 ∂_uμ ∂_vμ/(r|f|), of which the DTR relation is the thin-shell form; the in-out coupling 2/(r|f|) is uniformly bounded on the interior precisely when the gap is positive. This yields an a priori mass bound and, in the Ori thin-shell model, an e-folding rate bounded by the influx luminosity instead of tending to the inner-horizon surface gravity. Integrable-singularity interiors thus realize a class of sources for which the Poisson-Israel-Ori amplification channel is structurally inoperative in the models in which mass inflation was originally established.
ER  -

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