Static vacuum 3+1 black holes that cannot be put into stationary rotation

TL;DR

This paper proves that certain static vacuum black holes in 3+1 dimensions cannot be transformed into rotating stationary solutions, highlighting a new form of static rigidity in General Relativity.

Contribution

It establishes the first example of static rigidity, showing some static vacuum black holes cannot be deformed into rotating solutions, especially for specific MKN configurations.

Findings

Some MKN static black holes cannot be rotated into stationary solutions.

Static rigidity is demonstrated for particular MKN solutions with small pole separation.

These solutions are regular, asymptotically Kasner, with no singularities or struts.

Abstract

We prove that some of the static Myers/Korotkin-Nicolai (MKN) vacuum 3+1 static black holes cannot be put into stationary rotation. Namely, they cannot be deformed into axisymmetric stationary vacuum black holes with non-zero angular momentum. We also prove that this occurs in particular for those MKN solutions for which the distance along the axis between the two poles of the horizon is sufficiently small compared to the square root of its area. The MKN solutions, sometimes called periodic Schwarzschild, are physically regular, have no struts or singularities, but are asymptotically Kasner. The static rigidity presented here appears to be the first in the literature of General Relativity.