Geometric horizons in binary black hole mergers

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-ε 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.