4-dimensional dilaton black holes with cosmological constant

TL;DR

This paper investigates static, spherically symmetric dilaton black hole solutions with a cosmological constant, deriving a power series solution and analyzing the maximum number of horizons, revealing notable differences from known Reissner-Nordström-de Sitter black holes.

Contribution

It provides a formal power series solution for dilaton black holes with cosmological constant and proves bounds on the number of horizons, highlighting differences from classical solutions.

Findings

Maximum of 2 horizons for positive cosmological constant

Maximum of 1 horizon for negative cosmological constant

Contrast with Reissner-Nordström-de Sitter black holes with 3 horizons

Abstract

Static and spherically symmetric black hole solutions with non-zero cosmological constant are investigated. A formal power series solution is found. It is proved that the number of regular horizons is less than or equal to 2 for positive cosmological constant and is less than or equal to 1 for negative cosmological constant. This shows a striking contrast to the fact that the Reissner-Nordstr{\o}m-de Sitter black hole with positive cosmological horizon has 3 regular horizons.