Massive quantum divergence on the Cauchy horizon of a black hole

• URL: http://arxiv.org/abs/2609.10755v2
• Date: Fri, 11 Sep 2026 17:56:00 GMT
• Title: Massive quantum divergence on the Cauchy horizon of a black hole
• Abstract summary: We investigate a quantum massive scalar field in the interior of a charged and spherically-symmetric black hole.<n>We show that the vacuum polarization as well as the angular components of the quantum stress-energy tensor diverge on the Cauchy horizon.
• Score: 0.5461938536945722
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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.

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