Gravity, axion Chern-Simons Einstein, and black holes

The low-energy limit of string theory involves an anomaly-removing correction of the action of Einstein-Hilbert, which defines a practical idea: Chern-Simons (CS) modified gravity. The CS correction composes of the product of a scalar field with the Pontryagin density, in which the scalar field is considered as a background field (non-dynamical formulation) or as an evolving field (dynamical formulation). Different solutions of Einstein's general relativity (GR) continue in the amended theory; a keyable exception is the Kerr metric, which has affected a search for rotating black hole solutions. In this study, we derive a black solution characterizing a rotating black hole within the non-dynamical and dynamical frame of CS axion Einstein gravity (CSAEG). The case of non-dynamical has no new physics different from GR, which is consistent with what is presented in the literature. The main merit of this study is that in the dynamical framework of CSAEG, we show that the scalar field has a dynamical value up to the first-order approximation and under some constraints between the unknown functions that characterize this theory. Moreover, we show that the function U that characterizes CS can help to weaken the singularity for the invariant *RR.