Twisted Black Hole Is Taub-NUT

TL;DR

This paper analyzes a proposed twisted black hole solution, revealing it is actually a Taub-NUT geometry with conical singularities and closed timelike curves, thus lacking physical viability despite initial claims of novelty.

Contribution

It clarifies that the purported twisted black hole is not a new solution but is equivalent to the known Taub-NUT geometry with inherent pathologies.

Findings

Presence of conical singularity along the rotation axis

Existence of closed timelike curves in the spacetime

The solution is equivalent to the Taub-NUT geometry

Abstract

Recently a purportedly novel solution of the vacuum Einstein field equations was discovered: it supposedly describes an asymptotically flat twisted black hole in 4-dimensions whose exterior spacetime rotates in a peculiar manner -- the frame dragging in the northern hemisphere is opposite from that of the southern hemisphere, which results in a globally vanishing angular momentum. Furthermore it was shown that the spacetime has no curvature singularity. We show that the geometry of this black hole spacetime is nevertheless not free of pathological features. In particular, it harbors a rather drastic conical singularity along the axis of rotation. In addition, there exist closed timelike curves due to the fact that the constant r and constant t surfaces are not globally Riemannian. In fact, none of these are that surprising since the solution is just the Taub-NUT geometry. As such, despite the original claim that the twisted black hole might have observational consequences, it cannot be.