A Type of Levi-Civita's Solution in Modified Gauss-Bonnet Gravity

TL;DR

This paper derives an exact cylindrically symmetric solution in modified Gauss-Bonnet gravity, generalizing Levi-Civita's vacuum solution, and interprets it as an exterior metric of a cosmic string, reducing to Einstein's solution when the coupling is zero.

Contribution

It provides the first exact solution in modified Gauss-Bonnet gravity for a cylindrically symmetric spacetime, extending Levi-Civita's solution to this modified theory.

Findings

The solution describes an isotropic perfect fluid configuration.

It reduces to Levi-Civita's vacuum solution when the Gauss-Bonnet coupling is zero.

The metric can be interpreted as the exterior of a cosmic string.

Abstract

In this letter we obtain an exact solution for cylindrically symmetric modified Gauss Bonnet gravity. This metric is a generalization of the vacuum solution of the Levi-Civita in the general relativity. It describes an isotropic perfect fluid one parameter family of the gravitational configurations which can be interpreted as the exterior metric of a cosmic string. By setting the Gauss-Bonnet coupling parameter to zero, we recover the vacuum solution in the Einstein gravity as well.