Geometric horizons in binary black hole mergers

TL;DR

This study numerically investigates the algebraic properties of the Weyl tensor during binary black hole mergers, providing evidence that a smooth geometric horizon can be consistently identified throughout the entire merger process.

Contribution

It introduces a numerical approach to identify a unique smooth geometric horizon in binary black hole mergers using algebraic properties of the Weyl tensor.

Findings

A geometric horizon can be identified throughout all merger stages.

The horizon is characterized by the vanishing of a complex scalar invariant.

Numerical evidence supports the conjecture of a smooth, algebraically special horizon.

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-$\varepsilon$ 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.