Renormalization of $\langleϕ^2\rangle$ at the inner horizon of rotating, accreting black holes

Tyler McMaken; Andrew J. S. Hamilton

doi:10.1103/PhysRevD.105.125020

paper

Renormalization of $⟨ ϕ^{2} ⟩$ at the inner horizon of rotating, accreting black holes

arXiv:2204.03224 · doi:10.1103/PhysRevD.105.125020

Abstract

Classically, the inner horizon of a perturbed, rotating black hole undergoes an instability known as mass inflation, wherein the spacetime curvature diverges as a result of hyper-relativistic crossing streams of ingoing and outgoing radiation. The generic outcome of this instability is currently believed to be a strong, spacelike singularity, potentially alongside a weak, null singularity surviving at late times. However, the quantum back-reaction in this regime has yet to be fully calculated for a realistic black hole spacetime. Here we consider a massless quantized scalar field $ϕ$ over the inflationary Kasner spacetime, a recently developed model for the inner horizon geometry of a rotating, accreting black hole. With this spacetime, we use numerical adiabatic regularization to calculate $⟨ ϕ^{2} ⟩_{ren}$ , the renormalized coincidence limit of the two-point correlation function, as a pointer to the behavior of the quantum stress-energy tensor. $⟨ ϕ^{2} ⟩_{ren}$ is generically found to be nonzero near the inner horizon, divergent where the curvature classically diverges, and larger for smaller black hole spins or accretion rates.

12 pages, 6 figures

Renormalization of $⟨ ϕ^{2} ⟩$ at the inner horizon of rotating, accreting black holes

Abstract

References in corpus (13)

Cited by in corpus (3)

Renormalization of ⟨ϕ2⟩ at the inner horizon of rotating, accreting black holes

Abstract

References in corpus (13)

Cited by in corpus (3)

Renormalization of $⟨ ϕ^{2} ⟩$ at the inner horizon of rotating, accreting black holes