Stationary vacuum black holes in 5 dimensions. Issue 8 (3rd August 2018)

• Record Type: Journal Article
• Authors: Khuri, Marcus; Weinstein, Gilbert; Yamada, Sumio
• Is Part Of: Communications in partial differential equations. Volume 43:Issue 8(2018)
• Page Start: 1205
• Page End: 1241
• Publication Date: 2018-08-03
• Subjects: Lens space -- non-spherical event horizons -- singular harmonic maps -- stationary black hole spacetime; Differential equations, Partial -- Periodicals; 515.353
• DOI: 10.1080/03605302.2018.1517791
• Languages: English
• ISSNs: 0360-5302

Abstract

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 ringS 1 × S 2, or the lens space L ( p, q ). The Einstein vacuum equations reduce to an axially symmetric harmonic map with prescribed singularities fromR 3 into the symmetric spaceS L ( 3, R ) / S O ( 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.