Charged black holes in compactified spacetimes

TL;DR

This paper constructs and analyzes a compactified version of the Reissner-Nordstrom-NUT black hole, revealing how electric and NUT charges influence singularities and providing detailed solutions with explicit parameters.

Contribution

It introduces a new compactified solution for charged black holes with NUT charge, extending previous Schwarzschild models and explicitly calculating key parameters of the asymptotic solutions.

Findings

NUT charge removes curvature singularity on the torus surrounding the horizon.

Explicit parameters for the periodic Levi-Civita solution are calculated.

Solution family exhibits a curvature singularity for nonzero electric charge without NUT charge.

Abstract

We construct and investigate a compactified version of the four-dimensional Reissner-Nordstrom-NUT solution, generalizing the compactified Schwarzschild black hole that has been previously studied by several workers. Our approach to compactification is based on dimensional reduction with respect to the stationary Killing vector, resulting in three-dimensional gravity coupled to a nonlinear sigma model. Using that the original non-compactified solution corresponds to a target space geodesic, the problem can be linearized much in the same way as in the case of no electric nor NUT charge. An interesting feature of the solution family is that for nonzero electric charge but vanishing NUT charge, the solution has a curvature singularity on a torus that surrounds the event horizon, but this singularity is removed when the NUT charge is switched on. We also treat the Schwarzschild case in a more complete way than has been done previously. In particular, the asymptotic solution (the Levi-Civita solution with the height coordinate made periodic) has to our knowledge only been calculated up to a determination of the mass parameter. The periodic Levi-Civita solution contains three essential parameters, however, and the remaining two are explicitly calculated here.