Uniqueness Theorem for 5-Dimensional Black Holes with Two Axial Killing Fields

Abstract

We show that two stationary, asymptotically flat vacuum black holes in 5 dimensions with two commuting axial symmetries are identical if and only if their masses, angular momenta, and their "rod structures" coincide. We also show that the horizon must be topologically either a 3-sphere, a ring, or a Lens-space. Our argument is a generalization of constructions of Morisawa and Ida (based in turn on key work of Maison) who considered the spherical case, combined with basic arguments concerning the nature of the factor manifold of symmetry orbits.

An inverse scattering formalism for STU supergravity

“…For this computation, group rotation is sufficient, but we expect that in more complicated situations, in particular for configurations involving three or more poles, one needs to develop some other algorithmic techniques to find appropriate vectors. In this regard, ideas from the interval structure [26][27][28] of gravitational solutions can be useful, but at the moment this remains an open challenging problem.…”

Spacetime Topology and the Laws of Black Hole-Soliton Mechanics

“…Due to (2) it proves convenient to consider all spacetime fields as functions on the two-dimensional orbit space B ≡ M/(R t × U(1) 2 ). B can be shown to be a simply connected manifold with boundary ∂B and corners [9]. In the interior, on the 1d boundary segments (except the part corresponding to the event horizon in the spacetime) and at the corners (where these segments intersect), the matrix of the scalar products of Killing fields g(m i , m j ) has rank 2, 1, 0 respectively.…”

Rotating black rings on Taub-NUT

“…So it allows us to apply the rod-structure formalism, following the prescription of [27,8] (see also [28,29]). In the Weyl-Papapetrou coordinates (ρ, z), which are related to the above C-metric-like coordinates by (2.5), the rod structure has three turning points:…”