New form of the Kerr-Newman solution

TL;DR

This paper introduces a new coordinate system for the Kerr-Newman black hole solution that is well-behaved at horizons and adaptable to different charge configurations, providing a unified and extended description of the spacetime.

Contribution

The authors develop a novel coordinate system for the Kerr-Newman solution that generalizes Doran and Eddington-Finkelstein coordinates, offering a global and physically intuitive description of charged rotating black holes.

Findings

Coordinates reduce to Doran coordinates when charge is zero.

Range of validity extends with increasing charge magnitude.

Coordinates become Eddington-Finkelstein in the limit of large charge.

Abstract

A new form of the Kerr-Newman solution is presented. The solution involves a time coordinate which represents the local proper time for a charged massive particle released from rest at spatial infinity. The chosen coordinates ensure that the solution is well-behaved at horizons and enable an intuitive description of many physical phenomena. If the charge of the particle $e = 0$, the coordinates reduce to Doran coordinates for the Kerr solution with the replacement $M \to M - Q^2/(2r)$, where $M$ and $Q$ are the mass and charge of the black hole, respectively. Such coordinates are valid only for $r \ge Q^2/(2M)$, however, which corresponds to the region that a neutral particle released from rest at infinity can penetrate. By contrast, for $e \neq 0$ and of opposite sign to $Q$, the new coordinates have a progressively extended range of validity as $|e|$ increases and tend to advanced Eddington-Finkelstein (EF) null coordinates as $|e| \to \infty$, hence becoming global in this limit. The Kerr solution (i.e.\ with $Q=0$) may also be written in terms of the new coordinates by setting $eQ = -\alpha$, where $\alpha$ is a real parameter unrelated to charge; in this case the coordinate system is global for all non-negative values of $\alpha$ and the limits $\alpha = 0$ and $\alpha \to \infty$ correspond to Doran coordinates and advanced EF null coordinates, respectively, without any need to transform between them.