Massive quantum divergence on the Cauchy horizon of a black hole
Abstract
We investigate a quantum massive scalar field in the interior of a charged and spherically-symmetric (Reissner-Nordström) black hole. We examine the behaviour for varying values of the black hole charge, field mass and coupling constant when the field is in two quantum states: Hartle-Hawking (representing a black hole in thermal equilibrium) and Unruh (representing a black hole evaporating via the emission of Hawking radiation). We show that the vacuum polarization as well as the angular components of the quantum stress-energy tensor diverge on the Cauchy horizon, in stark contrast to what happens for massless fields. We also calculate the energy fluxes in Eddington-Finkelstein coordinates {u,v}. We show that these fluxes on the Cauchy horizon do not generically vanish. This implies, in particular, that in regular, Kruskal coordinates {U,V} the ingoing flux diverges like V−2 on the Cauchy horizon (where V=0). This divergence suggests that its backreaction via the semiclassical Einstein equations would yield a strong singularity, as opposed to its weaker, classical counterpart. Interestingly, there are exceptions, in which the energy fluxes in Eddington-Finkelstein coordinates vanish: (i) in the extremal limit (where the black hole is maximally charged); (ii) certain fine-tuned regions of parameter space, where the fluxes change sign.
Related
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BibTeX
@misc{casals2026massive,
title = {{Massive quantum divergence on the Cauchy horizon of a black hole}},
author = {Marc Casals and Lorenzo Pisani and Peter Taylor},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.10755},
eprint = {2609.10755},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.10755},
}
RIS
TY - UNPB
TI - Massive quantum divergence on the Cauchy horizon of a black hole
AU - Marc Casals
AU - Lorenzo Pisani
AU - Peter Taylor
PY - 2026
DA - 2026/09/11
PB - arXiv
DO - 10.48550/arxiv.2609.10755
UR - https://arxiv.org/abs/2609.10755
AB - We investigate a quantum massive scalar field in the interior of a charged and spherically-symmetric (Reissner-Nordström) black hole. We examine the behaviour for varying values of the black hole charge, field mass and coupling constant when the field is in two quantum states: Hartle-Hawking (representing a black hole in thermal equilibrium) and Unruh (representing a black hole evaporating via the emission of Hawking radiation). We show that the vacuum polarization as well as the angular components of the quantum stress-energy tensor diverge on the Cauchy horizon, in stark contrast to what happens for massless fields. We also calculate the energy fluxes in Eddington-Finkelstein coordinates {u,v}. We show that these fluxes on the Cauchy horizon do not generically vanish. This implies, in particular, that in regular, Kruskal coordinates {U,V} the ingoing flux diverges like V^−2 on the Cauchy horizon (where V=0). This divergence suggests that its backreaction via the semiclassical Einstein equations would yield a strong singularity, as opposed to its weaker, classical counterpart. Interestingly, there are exceptions, in which the energy fluxes in Eddington-Finkelstein coordinates vanish: (i) in the extremal limit (where the black hole is maximally charged); (ii) certain fine-tuned regions of parameter space, where the fluxes change sign.
ER -