Global properties of static spherically symmetric charged dilaton spacetimes with a Liouville potential

TL;DR

This paper investigates the global characteristics of static spherically symmetric solutions in Einstein-Maxwell-dilaton systems with exponential potentials, revealing the non-existence of certain asymptotic solutions except for pure cosmological constants.

Contribution

It provides a comprehensive analysis of the global properties of these solutions, highlighting the limitations on their asymptotic behaviors in the presence of exponential dilaton potentials.

Findings

No asymptotically flat solutions with non-trivial potentials

No asymptotically de Sitter or anti-de Sitter solutions except for pure cosmological constant

Characterization of global properties of solutions in the Einstein-Maxwell-dilaton system

Abstract

We derive the global properties of static spherically symmetric solutions to the Einstein-Maxwell-dilaton system in the presence of an arbitrary exponential dilaton potential. We show that -- with the exception of a pure cosmological constant `potential' -- no asymptotically flat, asymptotically de Sitter or asymptotically anti-de Sitter solutions exist in these models.