Solutions of a slowly rotating Kerr flat-horizon black hole in dynamical Chern-Simons modified gravity

Abstract

Solutions pertaining to a Kerr black hole with a flat horizon undergoing gradual rotation are explored in the context of gravitational theories modified by dynamical Chern-Simons terms with cylindrical metrics, which approach asymptotically the anti de Sitter spacetime. It is shown that the cross-term of a metric component is unaffected by the perturbations of the Chern-Simons scalar independently of whether the dynamical Chern-Simons field equation is uncharged or charged with an electric field. From this result, it is ensured that the Chern-Simons scalar field can affect the spaces of the metric that approach asymptotically the flat spacetime only.