Apparent Horizons with Nontrivial Topology and the Hyperhoop Conjecture in Six-Dimensional Space-Times

Abstract: We investigate the validity of the hyperhoop conjecture, which claims to determine a necessary and sufficient condition for the formation of black hole horizons in higher-dimensional space-times. Here we consider momentarily static, conformally flat initial data sets each describing a gravitational field of uniform massive k-sphere sources, for k=1,2, on the five-dimensional Cauchy surface. The numerical result shows the validity of the hyperhoop conjecture for a wide range of model parameters. We also confirm for the first time the existence of an apparent horizon homeomorphism to S*2 x S2 or S1 x S*3, which is a higher-dimensional generalization of the black ring.