Infinite Volume of Noncommutative Black Hole Wrapped by Finite Surface

TL;DR

This paper demonstrates that in noncommutative spacetime, black hole volume becomes infinite while surface area remains finite, challenging the traditional statistical interpretation of black hole entropy.

Contribution

It shows that noncommutative geometry leads to infinite black hole volume, suggesting entropy may be independent of volume and challenging existing interpretations.

Findings

Black hole volume is infinite in noncommutative spacetime.

Surface area and entropy remain finite despite infinite volume.

Back reaction effects are negligible in this context.

Abstract

The volume of a black hole under noncommutative spacetime background is found to be infinite, in contradiction with the surface area of a black hole, or its Bekenstein-Hawking (BH) entropy, which is well-known to be finite. Our result rules out the possibility of interpreting the entropy of a black hole by counting the number of modes wrapped inside its surface if the final evaporation stage can be properly treated. It implies the statistical interpretation for the BH entropy can be independent of the volume, provided spacetime is noncommutative. The effect of radiation back reaction is found to be small and doesn't influence the above conclusion.