Entropy of BTZ black strings in the brick wall approach

TL;DR

This paper calculates the entropy of a scalar field around rotating BTZ black strings in an anti-de Sitter bulk using the brick wall model, confirming the Bekenstein-Hawking area law in both brane and bulk contexts.

Contribution

It provides the first explicit computation of scalar field entropy for rotating BTZ black strings within the brick wall framework, validating the area law in this setting.

Findings

Bekenstein-Hawking area law holds for the black string both on the brane and in the bulk.

Explicit entropy calculation matches the expected area law.

Supports the consistency of black string thermodynamics in AdS spacetimes.

Abstract

During the last few years, exact solutions that describe black holes that are bound to a two-brane in a four dimensional anti-de Sitter bulk have been constructed. In situations wherein there is a negative cosmological constant on the brane, for large masses, these solutions are exactly the rotating BTZ black holes on the brane and, in fact, describe rotating BTZ black strings in the bulk. We evaluate the canonical entropy of a free and massless scalar field (at the Hawking temperature) around the rotating BTZ black string using the brick wall model. We explicitly show that the Bekenstein-Hawking `area' law is satisfied both on the brane as well as in the bulk.