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

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.

Title is modified, paper shortened, to appear in Int.J.Mod.Phys. A

References in corpus (3)

• Black Hole Enthalpy and an Entropy Inequality for the Thermodynamic Volume
• How big is a black hole?
• The Hawking cascades of gravitons from higher-dimensional Schwarzschild black holes

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