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

Abstract

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