Godel-type Metrics in Various Dimensions II: Inclusion of a Dilaton Field

TL;DR

This paper extends Godel-type metrics by including a dilaton field, enabling the construction of exact solutions in higher-dimensional Einstein-Maxwell-dilaton theories and supergravity, broadening the scope of known solutions.

Contribution

It introduces a dilaton field into Godel-type metrics and demonstrates their use in solving complex field equations in higher-dimensional supergravity models.

Findings

Conformally transformed Godel-type metrics solve Einstein-Maxwell-dilaton-3-form theories in D >= 6.

Exact solutions to supergravity theories are obtained using these metrics.

Majumdar-Papapetrou metrics generalize naturally in higher dimensions.

Abstract

This is the continuation of an earlier work where Godel-type metrics were defined and used for producing new solutions in various dimensions. Here a simplifying technical assumption is relaxed which, among other things, basically amounts to introducing a dilaton field to the models considered. It is explicitly shown that the conformally transformed Godel-type metrics can be used in solving a rather general class of Einstein-Maxwell-dilaton-3-form field theories in D >= 6 dimensions. All field equations can be reduced to a simple "Maxwell equation" in the relevant (D-1)-dimensional Riemannian background due to a neat construction that relates the matter fields. These tools are then used in obtaining exact solutions to the bosonic parts of various supergravity theories. It is shown that there is a wide range of suitable backgrounds that can be used in producing solutions. For the specific case of (D-1)-dimensional trivially flat Riemannian backgrounds, the D-dimensional generalizations of the well known Majumdar-Papapetrou metrics of general relativity arise naturally.