Generalized Area Law under Multi-parameter Rotating Black Hole Spacetime

TL;DR

This paper derives a generalized area law for scalar field entropy in multi-parameter rotating black hole spacetimes across arbitrary dimensions, extending thermodynamic understanding without relying on specific black hole solutions.

Contribution

It introduces a general method to derive the scalar field entropy area law applicable to various rotating black holes in any dimension, independent of explicit metric solutions.

Findings

Derived a generalized Stefan-Boltzmann law for scalar fields.

Established a generalized area law for scalar field entropy.

Applied the law to Kerr-AdS black holes in 4 and 5 dimensions.

Abstract

We study the statistical mechanics for quantum scalar fields under the multi-parameter rotating black hole spacetime in arbitrary D dimensions. The method of analysis is general in the sense that the metric does not depend on the explicit black hole solutions. The generalized Stefan-Boltzmann's law for the scalar field is derived by considering the allowed energy region properly. Then the generalized area law for the scalar field entropy is derived by introducing the invariant regularization parameter in the Rindler spacetime. The derived area law is applied to Kerr-AdS black holes in four and five dimensions. Thermodynamic implication is also discussed.