A New Class of Exact Solutions in Einstein-Maxwell-dilaton Theory

TL;DR

This paper presents new exact, non-stationary solutions to five-dimensional Einstein-Maxwell-dilaton theory with a cosmological constant, revealing unique spacetime properties and extending previous solution classes.

Contribution

It introduces a novel class of exact solutions with distinct dilaton couplings, demonstrating their uniqueness and non-extendability to higher dimensions or simpler theories.

Findings

Solutions are conformally regular and depend on time and two spatial directions.

The solutions are unique in five dimensions and cannot be uplifted to higher-dimensional theories.

New solutions are constructed for equal coupling constants.

Abstract

We find new solutions to the five-dimensional Einstein-Maxwell-dilaton theory with cosmological constant where the dilaton field couples to the electromagnetic field as well as to the cosmological term with two different coupling constants. The five-dimensional spacetime is non-stationary and is a conformally regular spacetime, everywhere. Both the dilaton field and the electromagnetic field depends on time and two spatial directions. The cosmological constant takes positive, negative or zero value, depending on the value of coupling constant. We study the physical properties of the spacetime and show that the solutions are unique in five dimensions and can't be uplifted to higher-dimensional Einstein-Maxwell theory or Einstein gravity in presence of cosmological constant. Moreover, we construct new solutions to the theory where both coupling constants are equal.