Black Hole Scan

TL;DR

This paper investigates a class of gravitation theories with unique anti-de Sitter vacua, analyzing black hole solutions and their thermodynamic properties across different dimensions and parameters, revealing a minimum size for charged sources and two thermodynamic behavior classes.

Contribution

It introduces a systematic study of black holes in gravitation theories with fixed AdS vacua, identifying their properties and thermodynamics across various dimensions and parameters.

Findings

Black holes are found for each dimension and parameter k.

A minimum size for charged sources is predicted in all theories except General Relativity.

Thermodynamic behavior divides into two classes based on the relation between dimension and parameter k.

Abstract

Gravitation theories selected by requiring that they have a unique anti-de Sitter vacuum with a fixed cosmological constant are studied. For a given dimension d, the Lagrangians under consideration are labeled by an integer k=1,2,...,[(d-1)/2]. Black holes for each d and k are found and are used to rank these theories. A minimum possible size for a localized electrically charged source is predicted in the whole set of theories, except General Relativity. It is found that the thermodynamic behavior falls into two classes: If d-2k=1, these solutions resemble the three dimensional black hole, otherwise, their behavior is similar to the Schwarzschild-AdS_4 geometry.