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

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.