On the nonexistence of a vacuum black lens

Abstract

We demonstrate that five-dimensional, asymptotically flat, stationary and biaxisymmetric, vacuum black holes with lens space $L(n,1)$ topology, possessing the simplest rod structure, do not exist. In particular, we show that the general solution on the axes and horizon, which we recently constructed by exploiting the integrability of this system, must suffer from a conical singularity on the inner axis component. We give a proof of this for two distinct singly spinning configurations and numerical evidence for the generic doubly spinning solution.

v2: minor changes, published version; 23 pages, 3 figures

References in corpus (5)

• Uniqueness theorem for 5-dimensional black holes with two axial Killing fields
• Bicycling Black Rings
• Orthogonal black di-ring solution
• A supersymmetric black lens
• A stationary and biaxisymmetric four-soliton solution in five dimensions

Cited by in corpus (2)

• New construction of a charged dipole black ring by Harrison transformation
• Black Lenses in Kaluza-Klein Matter