Generalized Painleve-Gullstrand descriptions of Kerr-Newman black holes

TL;DR

This paper constructs new, singularity-free Painleve-Gullstrand metrics for Kerr-Newman black holes, ensuring real variables across parameters and improving descriptions for fermions and Hawking temperature calculations.

Contribution

It introduces a generalized, regular Painleve-Gullstrand metric for Kerr-Newman black holes with an extra tunable function for real variables, and analyzes vierbein fields for fermion descriptions.

Findings

Metrics are free of coordinate singularities.

All variables remain real for all parameters.

Correct Hawking temperature for Kerr black holes derived.

Abstract

Generalized Painleve-Gullstrand metrics are explicitly constructed for the Kerr-Newman family of charged rotating black holes. These descriptions are free of all coordinate singularities; moreover, unlike the Doran and other proposed metrics, an extra tunable function is introduced to ensure all variables in the metrics remain real for all values of the mass M, charge Q, angular momentum aM, and cosmological constant \Lambda > - 3/(a^2). To describe fermions in Kerr-Newman spacetimes, the stronger requirement of non-singular vierbein one-forms at the horizon(s) is imposed and coordinate singularities are eliminated by local Lorentz boosts. Other known vierbein fields of Kerr-Newman black holes are analysed and discussed; and it is revealed that some of these descriptions are actually not related by physical Lorentz transformations to the original Kerr-Newman expression in Boyer-Lindquist coordinates - which is the reason complex components appear (for certain ranges of the radial coordinate) in these metrics. As an application of our constructions the correct effective Hawking temperature for Kerr black holes is derived with the method of Parikh and Wilczek.