On smoothness of black saturns

Abstract

Abstract:We prove smoothness of the domain of outer communications (d.o.c.) of the Black Saturn solutions of Elvang and Figueras. We show that the metric on the d.o.c. extends smoothly across two disjoint event horizons with topology R × S 3 and R × S 1 × S 2 . We establish stable causality of the d.o.c. when the Komar angular momentum of the spherical component of the horizon vanishes, and present numerical evidence for stable causality in general.

Quantum Gravity via Supersymmetry and Holography

“…Remarkably, there exists an exact analytic solution to the 5D Einstein vacuum equations that realizes this Black Saturn configuration [32]. It is completely smooth everywhere outside and on the two horizons [32,33]. The Black Saturn solution was constructed using the inverse scattering technique.…”

Stable causality of Black Saturns

“…The numerator and the denominator of g ψψ , when written as polynomials in ρ, µ i , and some c 1 , c 2 , q contain tens of thousands monomials [1,2]. One may check with a direct Mathematica calculation that some non-trivial factors from the numerator and the denominator cancel and the original form of g ψψ may be simplified to…”

“…The functions H x , F are non-negative and they were defined in [2]. It follows from the analysis in [1] that zeros of H x F exist only for ρ = 0 and they cancel with the zeros of the numerator of g ψψ . The parameters c 1 , c 2 , q depend only on a i and do not depend on ρ, z.…”

“…provided the limit ρ → 0 + is carefully taken. If µ i (ρ = 0) = 0, then taking this limit should be preceded by the substitution µ i → ρ 2μ i , whereμ i > 0 [1]. The simplification (2.3) is a significant one.…”

“…The Black Saturn solution of Elvang and Figueras is a five dimensional black hole with disjoint event horizons with topology R × S 3 and R × S 1 × S 2 [1,2]. It describes a spherical black hole 1 surrounded by a black ring.…”