Quantum Fluctuations in the Interior of Black Holes and Backreactions

TL;DR

This paper investigates quantum field perturbations inside Schwarzschild black holes, calculating their energy-momentum contributions and backreactions on the geometry, suggesting potential observable effects from outside the black hole.

Contribution

It introduces a method to compute quantum backreactions in black hole interiors using regularization techniques and Einstein equations, revealing possible measurable quantum effects.

Findings

Quantum fluctuations influence the interior geometry significantly.

Regularization schemes effectively handle UV divergences.

Quantum effects may be detectable by external observers.

Abstract

We study the propagation of the quantum field perturbations in the interior of the Schwarzschild black hole. The interior of the black hole is like an anisotropic cosmological background which expands in one extended direction while contracting in azimuthal directions. Solving the quantum mode functions approximately, we calculate the expectation values of physical quantities such as the energy density $\langle \rho \rangle$ and pressure $\langle P\rangle$ as measured by an observer in the interior of the black hole. We employ a combination of the $\zeta$ function regularization and dimensional regularization schemes to regularize the UV divergences in the energy momentum tensor associated to these quantum perturbations. By solving the Einstein field equations, we calculate the quantum backreactions induced in the background geometry. We speculate that the effects of quantum fluctuations in the interior of the black hole can be measured by the exterior observer.