Toward a Complete Analysis of the Global Structure of Kerr-Newman Spacetime

TL;DR

This paper investigates the global structure of Kerr-Newman spacetime's submanifolds across different latitudes, revealing their maximal extensions and topologies, and discusses the method's applicability to other gravity theories.

Contribution

It introduces a new coordinate approach to analyze the global structure of Kerr-Newman submanifolds beyond the symmetry axis, extending Carter's analysis.

Findings

Maximal analytic extension of  heta = heta_0 submanifolds matches that of the symmetry axis.

The  heta = rac{\u03c0}{2} equatorial plane has Reissner-Nordstrom topology.

Method applicability to other Kerr-Newman-type solutions is discussed.

Abstract

An attempt is made to supplement Carter's partial investigation of the global structure of Kerr-Newman spacetime on the symmetry axis. Namely, the global structure of \theta = const. timelike submanifolds of Kerr-Newman metric starting from the symmetry axis all the way down to the equatorial plane are studied by introducing a new time coordinate slightly different from the usual Boyer-Lindquist time coordinate. It turns out that the maximal anaytic extension of \theta = \theta_0 (0 \leq \theta_0 < \pi/2) submanifolds is the same as that of the symmetry axis first studied by Carter whereas \theta = \pi/2 equatorial plane has the topology identical to that of the Reissner-Nordstrom spacetime. General applicability of this method to Kerr-Newman-type black hole solutions in other gravity theories is discussed as well.