2022/03/03 by Kubiznak, David, Tahamtan, Tayebeh, Svitek, Otakar · 1 citation
#FOS: Physical sciences #General Relativity and Quantum Cosmology (gr-qc) #High Energy Physics - Theory (hep-th)
paper · doi:10.48550/arxiv.2203.01919
We show how (at least in principle) one can construct electrically and magnetically charged slowly rotating black hole solutions coupled to non-linear electrodynamics (NLE). Our generalized Lense-Thirring ansatz is, apart from the static metric function f and the electrostatic potential ϕ inherited from the corresponding spherical solution, characterized by two new functions h (in the metric) and ω (in the vector potential) encoding the effect of rotation. In the linear Maxwell case, the rotating solutions are completely characterized by static solution, featuring h=(f-1)/r2 and ω=1. We show that when the first is imposed, the ansatz is inconsistent with any restricted (see below) NLE but the Maxwell electrodynamics. In particular, this implies that the (standard) Newman-Janis algorithm cannot be used to generate rotating solutions for any restricted non-trivial NLE. We present a few explicit examples of slowly rotating solutions in particular models of NLE, as well as briefly discuss the NLE charged Taub-NUT spacetimes.