Mauro Cambiaso Harb Universidad Nacional Autónoma de México
Abstract: Lorentz violating extensions of both general relativity and the standard model have been thoroughly studied for elucidating certain aspects of the would-be theory of quantum gravity. The case of general relativity extended by a Chern-Simons has gained considerable attention lately. So far, the effects of the Chern-Simons term as a source of torsion, and consequently its modification on geometry have been, to some extent, disregarded. Here we present a novel way of understanding a slowly rotating Kerr BH as a perturbation of the Schwarzschild BH, a problem that remained unsolved for a long time. We explicitly show that the breaking of spherical symmetry to axial symmetry occurs precisely due to the introduction of a vector field (the so called embedding coordinate) parallel to the axis of rotation of the Kerr BH at infinity. The method is such that: (a) it guarantees only second-order differential equations for the higher order corrections of the metric, contrary to previous formulations, where the order of the differential equation increased with the order of the perturbation (b) given any zeroth-order solution of the Einstein equations in vacuum, one can systematically explore the higher-order corrections implied and (c) it gives a very good control of the Bianchi identities together with the consistency conditions implied upon the equations of motion, at every order in the expansion.
