On the `Stationary Implies Axisymmetric' Theorem for Extremal Black Holes in Higher Dimensions

Understand

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.