Scalar Field Contribution to Rotating Black Hole Entropy

TL;DR

This paper investigates how scalar fields contribute to the entropy of rotating black holes in various dimensions, deriving a generalized area law and confirming it through multiple methods.

Contribution

It introduces a generalized area law for scalar field contributions to black hole entropy in rotating spacetimes, applicable across different dimensions and verified by Euclidean path integrals.

Findings

Derived a generalized area law for rotating black holes.

Confirmed the law using Euclidean path integral methods.

Discussed scalar field mass effects briefly.

Abstract

Scalar field contribution to entropy is studied in arbitrary D dimensional one parameter rotating spacetime by semiclassical method. By introducing the zenithal angle dependent cutoff parameter, the generalized area law is derived. The non-rotating limit can be taken smoothly and it yields known results. The derived area law is then applied to the Banados-Teitelboim-Zanelli (BTZ) black hole in (2+1) dimension and the Kerr-Newman black hole in (3+1) dimension. The generalized area law is reconfirmed by the Euclidean path integral method for the quantized scalar field. The scalar field mass contribution is discussed briefly.