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 ($\mathcal{D}$), characterizes a smooth foliation independent surface (horizon) associated with the BH. In the first simulation we investigate the level-$0$ sets of $\text{Re}(\mathcal{D})$ (since $\text{Im}(\mathcal{D})=0$) in the head-on collision of two unequal mass BHs. In the second simulation we shall investigate the level-$\epsilon$ sets of $|\mathcal{D}|$ 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.

Paper published as Letter in Class. Quant. Grav vol38, 17LT01 (2021). arXiv admin note: text overlap with arXiv:2101.09615

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