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 (), characterizes a smooth foliation independent surface (horizon) associated with the BH. In the first simulation we investigate the level-0 sets of (since ) in the head-on collision of two unequal mass BHs. In the second simulation we shall investigate the level-ɛ sets of 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.
Highlights
The event horizon of a black hole (BH) solution in General Relativity (GR) is defined as the boundary of the non-empty complement of the causal past of future null infinity; i.e., the region for which signals sent from the interior will never escape [1]
We have studied the conjecture that [13] if a BH spacetime is zeroth-order algebraically general, a geometric horizon (GH) in which the spacetime is algebraically special, and is identified by the vanishing of the complex scalar invariant D, characterizes a smooth foliation invariant surface associated with the BH
We have evaluated this conjecture by studying the GH numerically in the two physically relevant situations of the head-on collision of unequal mass BHs and two merging, equal mass and non-spinning BHs
Summary
The event horizon of a black hole (BH) solution in General Relativity (GR) is defined as the boundary of the non-empty complement of the causal past of future null infinity; i.e., the region for which signals sent from the interior will never escape [1]. Since we are primarily interested in numerical applications in 4D to study the (asymmetric) collapse or merger of real BHs, the relevent spacetimes are of general algebraic type away from the horizon. This can be applied to study where the covariant derivative of the Weyl tensor (∇W ) is of algebraically special type II/D. In the simulation of the head-on collision of two unequal mass non-spinning BHs axisymmetry is enforced and 6th order finite differencing on a uniform grid is used, and Brill-Lindquist initial data is considered, representing a BBH system at a moment of time-symmetry. Brill-Lindquist initial data with BH positions and momenta set up to satisfy the “QC-0” initial condition [31] is utilized
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