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

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. © 2013 Published by NRC Research Press.