Rotating Black Hole Entropy from Two Different Viewpoints

TL;DR

This paper compares black hole entropy calculations from two different viewpoints using the brick-wall method, revealing that the entropies coincide despite differences in superradiant mode contributions.

Contribution

It provides a novel comparison of entropy calculations from infinity and near-horizon observers, highlighting the role of superradiant modes in Kerr-Newman black holes.

Findings

Entropies from both viewpoints are identical.

Superradiant modes appear for infinity observer but not near horizon.

The method confirms the robustness of entropy calculations across viewpoints.

Abstract

Using the brick-wall method, we study the entropy of Kerr-Newman black hole from two different viewpoints, a rest observer at infinity and zero angular momentum observer near horizon. We investigate this with scalar field in the canonical quantization approach. An observer at infinity can take one of the two possible frequency ranges; one is with positive frequencies only and the other is with the whole range including negative frequencies. On the other hand, a zero angular momentum observer near horizon can take positive frequencies only. For the observer at infinity the superradiant modes appear in either choice of the frequency ranges and the two results coincide. For the zero angular momentum observer superradiant modes do not appear due to absence of ergoregion. The resulting entropies from the two viewpoints turn out to be the same.