Dilaton Black Holes in de Sitter or Anti-de Sitter Universe

TL;DR

This work constructs dilaton black hole solutions in de Sitter and anti-de Sitter backgrounds within Einstein–Maxwell–dilaton theory by employing a dilaton potential composed of a constant plus three Liouville-type terms. It provides explicit metric forms in both cosmic and Schwarzschild coordinates, derives the associated dilaton profile and the cosmological-dilaton potential V(φ) with V(φ) = (4/3)λ + (1/3)λ[ e^{2(φ−φ0)} + e^{−2(φ−φ0)} ], and establishes the relation D = Q^2 e^{2φ0}/(2M). The paper further generalizes to arbitrary dilaton–Maxwell coupling α, presents multi-dilaton–black-hole solutions in a de Sitter background, and analyzes horizon structures, highlighting qualitative differences from standard RN–(A)dS spacetimes. These results connect to SUSY potentials in special α, relate to higher-dimensional compactifications, and have potential implications for AdS/CFT and related dualities.

Abstract

Poletti and Wiltshire have shown that, with the exception of a pure cosmological constant, the solution of a dilaton black hole in the background of de Sitter or anti-de Sitter universe, does not exist in the presence of one Liouville-type dilaton potential. Here with the combination of three Liouville-type dilaton potentials, we obtain the dilaton black hole solutions in the background of de Sitter or anti-de Sitter universe.