First Law and a Variational Principle for Static Asymptotically Randall-Sundrum Black Holes

TL;DR

This paper introduces a new mass definition for asymptotically Randall-Sundrum black holes, establishes a first law of black hole mechanics including variations of key parameters, and proves a related variational principle for static solutions.

Contribution

It provides a novel intrinsic mass definition and a first law for RS black holes, along with a variational principle applicable to both RS1 and RS2 models.

Findings

Defined a thermodynamic volume and gravitational tension for RS black holes.

Proved a first law including variations of bulk cosmological constant, brane tensions, and interbrane distance.

Established a variational principle for static black holes in RS models.

Abstract

We give a new, intrinsic, mass definition for spacetimes asymptotic to the Randall-Sundrum braneworld models, RS1 and RS2. For this mass, we prove a first law for static black holes, including variations of the bulk cosmological constant, brane tensions, and RS1 interbrane distance. Our first law defines a thermodynamic volume and a gravitational tension that are braneworld analogs of the corresponding quantities in asymptotically AdS black hole spacetimes and asymptotically flat compactifications, respectively. We also prove the following related variational principle for asymptotically RS black holes: instantaneously static initial data that extremizes the mass yields a static black hole, for variations at fixed apparent horizon area, AdS curvature length, cosmological constant, brane tensions, and RS brane warp factors. This variational principle is valid with either two branes (RS1) or one brane (RS2), and is applicable to variational trial solutions.