New form of the Kerr-Newman solution

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 $e\ne 0$ 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.

4 pages, no figures, accepted as a Letter by PRD. Contains minor updates to match accepted version

References in corpus (5)

• Killing tensor and Carter constant for Painleve-Gullstrand form of Lense-Thirring spacetime
• Generalized Painlevé-Gullstrand metrics
• Unit-lapse versions of the Kerr spacetime
• Constant-$r$ geodesics in the Painleve-Gullstrand form of Lense-Thirring spacetime
• Painleve-Gullstrand coordinates versus Kerr spacetime geometry

Cited by in corpus (1)

• Charged rotating BTZ solution revisited: New coordinates and algebraic classifications