GEOMETRIC DUALITY AND CHERN–SIMONS MODIFIED GRAVITY

Abstract

We consider a theory which involves an extension of general relativity known as Chern–Simons modified gravity (CSMG). In this theory the standard Einstein–Hilbert action is extended with a gravitational Pontryagin density that is obtained from a divergence of a Chern–Simons topological current. The extended theory has the standard Schwarzchild metric as solution, however, only a perturbed Kerr metric holds solution. From the exact Kerr metric we construct dual metrics to search for rotating black hole solutions. The conditions on the Killing tensors associated with dual metrics entail nontrivial solutions to CSMG.