Thermodynamics of four-dimensional black objects in the warped compactification

TL;DR

This paper investigates the thermodynamics of four-dimensional black objects in braneworld models, deriving their properties using Euclidean methods, analyzing stability, and exploring phase transitions like the Hawking-Page transition.

Contribution

It provides a detailed thermodynamic analysis of black holes and strings in braneworld models, including new calculations of mass and stability, and discusses phase transitions in these settings.

Findings

Thermodynamic quantities are derived without regularization.

The Bekenstein-Hawking law and first law are confirmed.

BTZ black string is more stable than localized black holes in most cases.

Abstract

We reinvestigate the thermodynamics of black objects (holes and strings) in four-dimensional braneworld models that are originally constructed by Emparan, Horowitz and Myers based on the anti-de Sitter (AdS) C-metric. After proving the uniqueness of slicing the AdS C-metric, we derive thermodynamic quantities of the black objects by means of the Euclidean formulation and find that we have no necessity of requiring any regularization to calculate their classical action. We show that there exist the Bekenstein-Hawking law and the thermodynamic first law. The thermodynamic mass of the localized black hole on a flat brane is negative, and it differs from the one previously derived. We discuss the thermodynamic stabilities and show that the BTZ black string is more stable than the localized black holes in a canonical ensemble, except for an extreme case. We also find a braneworld analogue of the Hawking-Page transition between the BTZ black string and thermal AdS branes. The localized black holes on a de Sitter brane is discussed by considering Nariai instanton, comparing the study of "black cigar" in the five-dimensional braneworld model.