Charged Dilaton Black Holes with a Cosmological Constant

TL;DR

This paper investigates charged dilaton black holes with a cosmological constant, showing their existence conditions, numerically analyzing anti-de Sitter solutions, and exploring their thermodynamic properties, including extremal cases.

Contribution

It demonstrates the non-existence of such black holes with positive cosmological constant and provides a numerical study of anti-de Sitter solutions with detailed thermodynamics.

Findings

Solutions do not exist for positive cosmological constant.

Asymptotically anti-de Sitter black holes with a single horizon exist for negative cosmological constant.

Extremal solutions have zero entropy and infinite temperature.

Abstract

The properties of static spherically symmetric black holes, which are either electrically or magnetically charged, and which are coupled to the dilaton in the presence of a cosmological constant, are considered. It is shown that such solutions do not exist if the cosmological constant is positive (in arbitrary spacetime dimension >= 4). However, asymptotically anti-de Sitter black hole solutions with a single horizon do exist if the cosmological constant is negative. These solutions are studied numerically in four dimensions and the thermodynamic properties of the solutions are derived. The extreme solutions are found to have zero entropy and infinite temperature for all non-zero values of the dilaton coupling constant.