Godel-Type Metrics in Various Dimensions

TL;DR

This paper explores Godel-type metrics across various dimensions, demonstrating their use in generating exact solutions to Einstein-Maxwell equations, including black-hole-like objects and spacetimes with or without closed timelike/null curves.

Contribution

It introduces a method to construct charged dust solutions using Godel-type metrics in arbitrary dimensions, linking lower-dimensional Riemannian geometries to higher-dimensional Einstein-Maxwell solutions.

Findings

Godel-type metrics can produce exact solutions in supergravity theories.

Examples include spacetimes with closed timelike and null curves.

Certain solutions resemble black-hole-like objects in a Godel universe.

Abstract

Godel-type metrics are introduced and used in producing charged dust solutions in various dimensions. The key ingredient is a (D-1)-dimensional Riemannian geometry which is then employed in constructing solutions to the Einstein-Maxwell field equations with a dust distribution in D dimensions. The only essential field equation in the procedure turns out to be the source-free Maxwell's equation in the relevant background. Similarly the geodesics of this type of metric are described by the Lorentz force equation for a charged particle in the lower dimensional geometry. It is explicitly shown with several examples that Godel-type metrics can be used in obtaining exact solutions to various supergravity theories and in constructing spacetimes that contain both closed timelike and closed null curves and that contain neither of these. Among the solutions that can be established using non-flat backgrounds, such as the Tangherlini metrics in (D-1)-dimensions, there exists a class which can be interpreted as describing black-hole-type objects in a Godel-like universe.