Exact Solutions in Five-Dimensional Axi-dilaton Gravity with Euler-Poincare Term

TL;DR

This paper derives exact solutions for five-dimensional axi-dilaton gravity with an Euler-Poincare term, revealing classes of time-dependent and static solutions, including black holes with axion charge, and confirms Birkhoff's theorem in this context.

Contribution

It provides explicit exact solutions in five-dimensional axi-dilaton gravity with higher curvature terms, extending understanding of static and dynamic spacetimes in this theory.

Findings

Time-dependent solutions with spherical or hyperboloidal symmetry identified.

Static solutions including black holes with axion charge found.

Birkhoff's staticity theorem validated in axi-dilaton gravity.

Abstract

We examine the effective field equations that are obtained from the axi-dilaton gravity action with a second order Euler-Poincare term and a cosmological constant in all higher dimensions. We solve these equations for five-dimensional spacetimes possessing homogeneity and isotropy in their three-dimensional subspaces. For a number of interesting special cases we show that the solutions fall into two main classes: The first class consists of time-dependent solutions with spherical or hyperboloidal symmetry which require certain fine-tuning relations between the coupling constants of the model and the cosmological constant. Solutions in the second class are locally static and prove the validity of Birkhoff's staticity theorem in the axi-dilaton gravity. We also give a special class of static solutions, among them the well-known black hole solutions in which the usual electric charge is superseded by an axion charge.