A type of Levi–Civita solution in modified Gauss–Bonnet gravity

Abstract

Herein we obtain an exact solution for cylindrically symmetric modified Gauss–Bonnet gravity. This metric is a generalization of the vacuum solution of Levi–Civita in 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.