A Variational Principle for Asymptotically Randall-Sundrum Black Holes

TL;DR

This paper establishes a variational principle for asymptotically Randall-Sundrum black holes, linking extremizing mass in initial data to static black hole solutions under fixed physical parameters.

Contribution

It introduces a variational principle applicable to RS black holes with one or two branes, based on the first law of black hole mechanics, for the first time.

Findings

Valid for both RS1 and RS2 models.

Applicable to variational trial solutions.

Connects extremizing mass to static solutions.

Abstract

We prove the following variational principle for asymptotically Randall-Sundrum (RS) black holes, based on the first law of black hole mechanics: 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.