On the global structure of the Pomeransky–Senkov black holes

Abstract

We construct analytic extensions of the Pomeransky-Senkov metrics with multiple Killing horizons and asymptotic regions. We show that, in our extensions, the singularities associated to an obstruction *

Space-time diagrammatics

“…We hope to return to this issue in the future. We expect the corresponding projection diagram to look like that for Kerranti de Sitter space-time of Figure 3.11, with r = ∞ there replaced by y = −1, r = −∞ replaced by y = 1 with an appropriate analytic continuation of the metric to positive y's (compare [7]), r + replaced by y h and r − replaced by y c . The shaded regions in the negative region there might be non-connected for some values of parameters, and always extend to the boundary at infinity in the relevant diamond [7].…”

“…The positive-definiteness of ( * * ) for y > y c follows from [7,10]. Note that g ψψ < 0 would give a timelike Killing vector ∂ ψ , and that g ϕϕ g ψψ − g 2 ψϕ < 0 would lead to some combination of the periodic Killing vectors ∂ ϕ and ∂ ψ being timelike, so the term ( * * ) in (3.82) is non-negative on any region where there are no obvious causality violations.…”

Mass–Angular-Momentum Inequality For Black Ring Spacetimes

“…According to [22,23], the maximal constant time slices in the domain of outer communication of the stationary black ring family are diffeomorphic to…”

Degenerating Black Saturns

“…We have thus exhausted the possibility of constructing a smooth extremal Black Saturn configuration in the family of solutions of Elvang-Figueras. This outcome is in consent with the known properties of 4+1-dimensional black holes. Both spherical black holes [2] and black rings [13,14] require two non-vanishing angular momenta to admit smooth extremal configurations. Unfortunately, the Black Saturn solution of Elvang-Figueras has angular momentum in a single plane only and it is not clear if doubly-spinning components can at all be kept in balance [1].…”