Geometric horizons in binary black hole mergers

Abstract

Abstract We numerically study the algebraic properties of the Weyl tensor through the merger of two non-spinning black holes (BHs). We are particularly interested in the conjecture that for such a vacuum spacetime, which is zeroth-order algebraically general, a geometric horizon (GH), on which the spacetime is algebraically special and which is identified by the vanishing of a complex scalar invariant ( D ), characterizes a smooth foliation independent surface (horizon) associated with the BH. In the first simulation we investigate the level-0 sets of Re ( D ) (since Im ( D ) = 0 ) in the head-on collision of two unequal mass BHs. In the second simulation we shall investigate the level-ɛ sets of | D | through a quasi-circular merger of two non-spinning, equal mass BHs. The numerical results, as displayed in the figures presented, provide evidence that a (unique) smooth GH can be identified throughout all stages of the binary BH merger.