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

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 an ${\mathrm{AdS}}_{2}\ifmmode\times\else\texttimes\fi{}{S}^{3}$ 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.