Dyonic dilaton black holes

TL;DR

This paper investigates static spherically symmetric black holes with both electric and magnetic charges coupled to a dilaton field, analyzing their existence, properties, and horizons in various cosmological constant scenarios.

Contribution

It demonstrates the non-existence of certain dyonic dilaton black hole solutions for positive Lambda and explores the existence and characteristics of solutions for negative and zero Lambda, including numerical analysis.

Findings

Asymptotically flat solutions have two horizons for specific dilaton coupling values.

Asymptotically anti-de Sitter solutions with non-trivial dilaton exist for Lambda < 0.

Extreme solutions have zero Hawking temperature regardless of dilaton coupling.

Abstract

The properties of static spherically symmetric black holes, which are both electrically and magnetically charged, and which are coupled to the dilaton in the presence of a cosmological constant, Lambda, are considered. It is shown that apart from the Reissner-Nordstrom-de Sitter solution with constant dilaton, such solutions do not exist if Lambda > 0 (in arbitrary spacetime dimension >=4 ). However, asymptotically anti-de Sitter dyonic black hole solutions with a non-trivial dilaton do exist if Lambda < 0. Both these solutions and the asymptotically flat (Lambda = 0) solutions are studied numerically for arbitrary values of the dilaton coupling parameter, g_0, in four dimensions. The asymptotically flat solutions are found to exhibit two horizons if g_0 = 0, 1, \sqrt{3}, \sqrt{6}, ..., \sqrt{n(n+1)/2},..., and one horizon otherwise. For asymptotically anti-de Sitter solutions the result is similar, but the corresponding values of g_0 are altered in a non-linear fashion which depends on Lambda and the mass and charges of the black holes. All dyonic solutions with Lambda <= 0 are found to have zero Hawking temperature in the extreme limit, however, regardless of the value of g_0.