2 research outputs found
On the `Stationary Implies Axisymmetric' Theorem for Extremal Black Holes in Higher Dimensions
All known stationary black hole solutions in higher dimensions possess
additional rotational symmetries in addition to the stationary Killing field.
Also, for all known stationary solutions, the event horizon is a Killing
horizon, and the surface gravity is constant. In the case of non-degenerate
horizons (non-extremal black holes), a general theorem was previously
established [gr-qc/0605106] proving that these statements are in fact generally
true under the assumption that the spacetime is analytic, and that the metric
satisfies Einstein's equation. Here, we extend the analysis to the case of
degenerate (extremal) black holes. It is shown that the theorem still holds
true if the vector of angular velocities of the horizon satisfies a certain
"diophantine condition," which holds except for a set of measure zero.Comment: 30pp, Latex, no figure