Some exact solutions with torsion in 5-D Einstein-Gauss-Bonnet gravity

TL;DR

This paper derives exact solutions with torsion in 5-D Einstein-Gauss-Bonnet gravity, revealing specific geometric structures and relations among coupling constants, including an AdS2×S3 solution analogous to Bertotti-Robinson space-time.

Contribution

It presents new exact solutions with torsion in 5-D Einstein-Gauss-Bonnet gravity, including a novel relation among coupling constants and an AdS2×S3 solution with physical interpretation.

Findings

Solutions have a cross product structure of constant curvature manifolds.

Derived a relation among coupling constants for nontrivial torsion solutions.

Found an AdS2×S3 solution analogous to Bertotti-Robinson space-time.

Abstract

Exact solutions with torsion in Einstein-Gauss-Bonnet gravity are derived. These solutions have a cross product structure of two constant curvature manifolds. The equations of motion give a relation for the coupling constants of the theory in order to have solutions with nontrivial torsion. This relation is not the Chern-Simons combination. One of the solutions has a $AdS_2\times S^3$ structure and is so the purely gravitational analogue of the Bertotti-Robinson space-time where the torsion can be seen as the dual of the covariantly constant electromagnetic field.