On regular frames near rotating black holes

Abstract

© 2018, Springer Science+Business Media, LLC, part of Springer Nature. We consider the metric of a generic axially symmetric rotating stationary black hole. The general approach is developed that enables us to construct coordinate frame regular near the horizon. As explicit examples, the Kerr and Kerr–Newmann-(anti-)de Sitter metrics are considered. It is shown how the rotational versions of the Painlevé–Gullstrand and Doran coordinates appear in this scheme as particular cases. For the 2 + 1 version of the metric the direct generalization of the Lemaître coordinate system is obtained. It is shown that the possibility of introducing a regular frame is indirectly related to the constancy of a black hole angular velocity and the rate with which the metric coefficient responsible for the rotation of spacetime tends to it.