Interior volume of ($1+D$) dimensional Schwarzschild black hole

TL;DR

This paper calculates the maximum interior volume of higher-dimensional Schwarzschild black holes, showing it increases during evaporation but at a decreasing rate with more spatial dimensions, potentially stabilizing for large D.

Contribution

It extends the analysis of black hole interior volume growth during evaporation to higher dimensions, revealing a decelerating increase and possible volume stabilization at large D.

Findings

Interior volume increases during evaporation in higher dimensions.

The rate of volume increase decreases as the number of spatial dimensions grows.

For large D, the interior volume approaches a constant value.

Abstract

We calculate the maximum interior volume, enclosed by the event horizon, of a ($1+D$)-dimensional Schwarzschild black hole. Taking into account the mass change due to Hawking radiation, we show that the volume increases towards the end of the evaporation. This fact is not new as it has been observed earlier for four dimensional case. The interesting point we observe is that this increase rate decreases towards the higher value of space dimensions $D$; i.e. it is a decelerated expansion of volume with the increase of spacial dimensions. This implies that for a sufficiently large $D$, the maximum interior volume does not change. The possible implications of these results are also discussed.