Quantum Evaporating Black Holes in Higher Dimensions

TL;DR

This paper investigates quantum effects on higher-dimensional Schwarzschild black holes, revealing dimension-dependent mass loss rates and unique wave function behaviors near singularities, contrasting with classical semiclassical predictions.

Contribution

It extends quantum analysis of black hole evaporation to higher dimensions, showing altered mass loss rates and wave function properties compared to four-dimensional cases.

Findings

Mass loss rate scales as 1/r^{N-1} in higher dimensions.

Wave function is singular at the singularity due to quantum fluctuations.

Quantum formalism differs from semiclassical results in higher dimensions.

Abstract

We study an $N + 1$ dimensional generalization of the Schwarzschild black hole from the quantum mechanical viewpoint. It is shown that the mass loss rate of this higher dimensional black hole due to the black hole radiation is proportional to $1 \over r^{N-1}$ where $r$ is the radial coordinate. This fact implies that except in four dimensions the quantum formalism developed in this letter gives a different result with respect to the mass loss rate from the semiclassical formalism where the Stefan-Bolzmann formula for a blackbody radiation is used. As shown previously in the study of the four dimensional Schwarzschild metric, the wave function in this case has also quite curious features that it is singular owing to strong quantum fluctuation of the gravitational field at the singularity while completely regular in the other regions of the spacetime.