Twisted Black Hole Is Taub-NUT

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.