Scalar field excited around a rapidly rotating black hole in Chern-Simons modified gravity

TL;DR

This paper investigates the behavior of a scalar field in the vicinity of a rapidly rotating black hole within dynamical Chern-Simons modified gravity, revealing divergences at the inner horizon under certain boundary conditions.

Contribution

It provides an analytical and numerical solution for the Chern-Simons scalar field around a rotating black hole, highlighting issues at the inner horizon.

Findings

Scalar field diverges at the inner horizon

Solutions obtained analytically and numerically

Boundary conditions affect scalar field regularity

Abstract

We discuss a Chern-Simons (CS) scalar field around a rapidly rotating black hole in dynamical CS modified gravity. The CS correction can be obtained perturbatively by considering the Kerr spacetime to be the background. We obtain the CS scalar field solution around the black hole analytically and numerically, assuming a stationary and axisymmetric configuration. The scalar field diverges on the inner horizon when we impose the boundary condition that the scalar field is regular on the outer horizon and vanishes at infinity. Therefore, the CS scalar field becomes problematic on the inner horizon.