The hoop conjecture for black rings

A precise formulation of the hoop conjecture for four-dimensional spacetimes proposes that the Birkhoff invariant beta for an apparent horizon in a spacetime with mass M should satisfy beta <= 4 pi M. The invariant beta is the least maximal length of any sweepout of the 2-sphere apparent horizon by circles. An analogous conjecture in five spacetime dimensions was recently formulated, asserting that the Birkhoff invariant beta for S-1 x S-1 sweepouts of the apparent horizon should satisfy beta <= 16/3 pi M. Although this hoop inequality was formulated for conventional five-dimensional black holes with 3-sphere horizons, we show here that it is also obeyed by a wide variety of black rings, where the horizon instead has S-2 x S-1 topology. (C) 2013 Elsevier B.V. All rights reserved.