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arXiv · 1711.05229

Stationary Vacuum Black Holes in 5 Dimensions

Marcus Khuri·Gilbert Weinstein·Sumio Yamada
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Abstract

We study the problem of asymptotically flat bi-axially symmetric stationary solutions of the vacuum Einstein equations in $5$-dimensional spacetime. In this setting, the cross section of any connected component of the event horizon is a prime $3$-manifold of positive Yamabe type, namely the $3$-sphere $S^3$, the ring $S^1\times S^2$, or the lens space $L(p,q)$. The Einstein vacuum equations reduce to an axially symmetric harmonic map with prescribed singularities from $\mathbb{R}^3$ into the symmetric space $SL(3,\mathbb{R})/SO(3)$. In this paper, we solve the problem for all possible topologies, and in particular the first candidates for smooth vacuum non-degenerate black lenses are produced. In addition, a generalization of this result is given in which the spacetime is allowed to have orbifold singularities. We also formulate conditions for the absence of conical singularities which guarantee a physically relevant solution.

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Marcus Khuri, Gilbert Weinstein, Sumio Yamada. 2017-11-14. Stationary Vacuum Black Holes in 5 Dimensions. https://arxiv.org/abs/1711.05229

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