## Faculty Scholarship

Article

2017

#### Abstract

We solve the Hamiltonian and momentum constraints of general relativity for two black-holes with nearly extremal spins and relativistic boosts in the puncture formalism. We use a non-conformally-flat ansatz with an attenuated superposition of two Lorentz-boosted, conformally-Kerr or conformally-Schwarzschild 3-metrics and their corresponding extrinsic curvatures. We compare evolutions of these data with the standard Bowen-York conformally-flat ansatz (technically limited to intrinsic spins $$\chi=S/M^2_{\text{ADM}}=0.928$$ and boosts $$P/M_{\text{ADM}}=0.897$$), finding, typically, an order of magnitude smaller burst of spurious radiation and agreement with inspiral and merger. As a first case study, we evolve two equal-mass black-holes from rest with an initial separation of $$d=12M$$ and spins $$\chi_i=S_i/m_i^2=0.99$$, compute the waveforms produced by the collision, the energy and angular momentum radiated, and the recoil of the final remnant black-hole. We find that the black-hole trajectories curve at close separations, leading to the radiation of angular momentum. We also study orbiting non-spinning and moderate-spin black-hole binaries and compare these with standard Bowen-York data. We find a substantial reduction in the non-physical initial burst of radiation which leads to cleaner waveforms. Finally, we study the case of orbiting binary black hole systems with spin magnitude $$\chi_i=0.95$$ in an aligned configuration and compare waveform and final remnant results with those of the SXS collaboration, finding excellent agreement. This represent the first moving puncture evolution of orbiting and spinning black holes exceeding the Bowen-York limit. Finally, we study different choices of the initial lapse and lapse evolution equation in the moving puncture approach to improve the accuracy and efficiency of the simulations.

#### Source Citation

Ruchlin, Ian., Healy, James., Lousto, Carlos O., & Zlochower, Yosef. (2017). Puncture Initial Data For Black-Hole Binaries With High Spins And High Boosts. Physical Review D - Particles, Fields, Gravitation, and Cosmology, 95(2). http://doi.org/10.1103/PhysRevD.95.024033

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