Inside the Schwarzschild-Tangherlini black holes

TL;DR

This paper investigates quantum effects inside Schwarzschild-Tangherlini black holes, revealing how quantum fields influence anisotropy and curvature, with results depending on spacetime dimension and coupling type.

Contribution

It provides the first semiclassical solutions for the interior of higher-dimensional black holes with quantum scalar fields, analyzing anisotropy and curvature behavior.

Findings

Quantum effects tend to isotropize the interior in 4 and 5 dimensions.

In 6 and 7 dimensions, quantum effects increase anisotropy.

Quantum perturbations initially increase curvature growth.

Abstract

The first-order semiclassical Einstein field equations are solved in the interior of the Schwarzschild-Tangherlini black holes. The source term is taken to be the stress-energy tensor of the quantized massive scalar field with arbitrary curvature coupling calculated within the framework of the Schwinger-DeWitt approximation. It is shown that for the minimal coupling the quantum effects tend to isotropize the interior of the black hole (which can be interpreted as an anisotropic collapsing universe) for D=4 and 5, whereas for D=6 and 7 the spacetime becomes more anisotropic. Similar behavior is observed for the conformal coupling with the reservation that for D=5 isotropization of the spacetime occurs during (approximately) the first 1/3 of the lifetime of the interior universe. On the other hand, we find that regardless of the dimension, the quantum perturbations initially strengthen the grow of curvature and its later behavior depends on the dimension and the coupling. It is shown that the Karlhede's scalar can still be used as a useful device for locating the horizon of the quantum-corrected black hole, as expected.