Accelerating NUT black holes

Abstract

We present and analyze a class of exact spacetimes which describe accelerating black holes with a Newman-Unti-Tamburino (NUT) parameter. First, by two independent methods we verify that the intricate metric found by Chng, Mann, and Stelea in 2006 indeed solves Einstein's vacuum field equations of general relativity. We explicitly calculate all components of the Weyl tensor and determine its algebraic structure. As it turns out, it is actually of algebraically general type I with four distinct principal null directions. It explains why this class of solutions has not been (and could not be) found within the large Pleba\ifmmode \acute{n}\else \'{n}\fi{}ski--Demia\ifmmode \acute{n}\else \'{n}\fi{}ski family of type D spacetimes. Then we transform the solution into a much more convenient metric form which explicitly depends on three physical parameters: mass $m$, acceleration $\ensuremath{\alpha}$, and the NUT parameter $l$. These parameters can independently be set to zero, recovering thus the well-known spacetimes in standard coordinates, namely the $C$-metric, the Taub--NUT metric, the Schwarzschild metric, and flat Minkowski space in spherical coordinates. Using this new metric, we investigate main physical and geometrical properties of such accelerating NUT black holes. In particular, we localize and study four Killing horizons (two black-hole plus two acceleration horizons) and carefully investigate the curvature. Employing the scalar invariants we prove that there are no curvature singularities whenever the NUT parameter is nonzero. We identify asymptotically flat regions and relate them to conformal infinities. This leads to a complete understanding of the global structure of the spacetimes: each accelerating NUT black hole is a ``throat'' which connects ``our universe'' with a ``parallel universe.'' Moreover, the analytic extension of the boost-rotation metric form reveals that there is a pair of such black holes (with four asymptotically flat regions). They uniformly accelerate in opposite directions due to the action of rotating cosmic strings or struts located along the corresponding two axes. Rotation of these sources is directly related to the NUT parameter. In their vicinity there are pathological regions with closed timelike curves.