  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. Other than axisymmetry, no assumptions are made on the
possible deformations. The phenomenon occurs in particular for those MKN
solutions for which the distance along the axis between the two horizon's poles
is sufficiently small compared to the square root of its area. The MKN
solutions, sometimes called periodic Schwarzschild, are physically regular but
asymptotically Kasner.
  The static rigidity presented here appears to be the first in the literature
of General Relativity.
