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

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.

Initial value formulation of dynamical Chern-Simons gravity

“…[37] and [39] that upon linearization around a Schwarzschild or slowly rotating BH background, respectively, the dCS field equations admit superluminal mode solutions, which are damped away. Studies of dCS gravity in the background of a Kerr BH revealed that the scalar field diverges on the inner horizon [18]. As described in Sec.…”

“…No complete solution for a rotating BH in dCS theory is known, but see Refs. [12][13][14][15][16][17][18][19] for perturbative calculations. Exploring dynamical BH solu tions provides the possibility to explore gravity in the strong-field regime.…”

“…We might furthermore insist on causality, or finite propagation speeds of information. While the linear sta bility of specific solutions has been studied [15,18,[37][38][39] (see Refs. [40] and [41] for similar studies in Gauss-Bonnet and in Lovelock theories), it is not known whether or not dCS gravity makes sense as a time evolution system.…”

“…(17) For completeness we give also the time derivative of the magnetic field, d,Bl = aK B' -[D x (aE)}1 + CpBl. (18) This equation is independent of any particular choice of model for the electromagnetic field, because it follows directly from Vb*Fab -0. Finally, the constraint equation…”

Anomaly-induced effective action and Chern–Simons modification of general relativity

“…Recently, the post-GR corrections for the dynamic model has been considered through the study of rapidly rotating black holes in the decoupling limit [34,35]. Such work is important because of the possibility to constraint the theory in the strong field regime.…”