On the nonexistence of a vacuum black lens

We demonstrate that five-dimensional, asymptotically flat, stationary and bi-axisymmetric, 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.

Automated summary

We demonstrate that no five-dimensional black holes exist with lens space L(n, 1) topology and the simplest rod structure. The general solution we constructed on the axes and horizon will have a conical singularity on the inner axis component, as proven for two distinct singly spinning configurations and numerically evidenced for the generic doubly spinning solution.