Numerical relativity of compact binaries in the 21st century.

We review the dramatic progress in the simulations of compact objects and compact-object binaries that has taken place in the first two decades of the twenty-first century. This includes simulations of the inspirals and violent mergers of binaries containing black holes and neutron stars, as well as simulations of black-hole formation through failed supernovae and high-mass neutron star-neutron star mergers. Modeling such events requires numerical integration of the field equations of general relativity in three spatial dimensions, coupled, in the case of neutron-star containing binaries, with increasingly sophisticated treatment of fluids, electromagnetic fields, and neutrino radiation. However, it was not until 2005 that accurate long-term evolutions of binaries containing black holes were even possible (Pretorius 2005 Phys. Rev. Lett. 95 121101, Campanelli et al 2006 Phys. Rev. Lett. 96 111101, Baker et al 2006 Phys. Rev. Lett. 96 111102). Since then, there has been an explosion of new results and insights into the physics of strongly-gravitating system. Particular emphasis has been placed on understanding the gravitational wave and electromagnetic signatures from these extreme events. And with the recent dramatic discoveries of gravitational waves from merging black holes by the Laser Interferometric Gravitational Wave Observatory and Virgo, and the subsequent discovery of both electromagnetic and gravitational wave signals from a merging neutron star-neutron star binary, numerical relativity became an indispensable tool for the new field of multimessenger astronomy.

Hangup kicks: still larger recoils by partial spin-orbit alignment of black-hole binaries.

We revisit the scenario of the gravitational radiation recoil acquired by the final remnant of a black-hole-binary merger by studying a set of configurations that have components of the spin both aligned with the orbital angular momentum and in the orbital plane. We perform a series of 42 new full numerical simulations for equal-mass and equal-spin-magnitude binaries. We extend previous recoil fitting formulas to include nonlinear terms in the spins and successfully include both the new and known results. The new predicted maximum velocity approaches 5000 km/s for spins partially aligned with the orbital angular momentum, which leads to an important increase of the probabilities of large recoils in generic astrophysical mergers. We find non-negligible probabilities for recoils of several thousand km/s from accretion-aligned binaries.

Orbital evolution of extreme-mass-ratio black-hole binaries with numerical relativity.

We perform the first fully nonlinear numerical simulations of black-hole binaries with mass ratios 100∶1. Our technique is based on the moving puncture formalism with a new gauge condition and an optimal choice of the mesh refinement. The evolutions start with a small nonspinning black hole just outside the ISCO that orbits twice before plunging. We compute the gravitational radiation, as well as the final remnant parameters, and find close agreement with perturbative estimates. We briefly discuss the relevance of these simulations for Advanced LIGO, third-generation ground-based detectors, LISA observations, and self-force computations.

Intermediate-mass-ratio black-hole binaries: numerical relativity meets perturbation theory.

We study black-hole binaries in the intermediate-mass-ratio regime 0.01≲q≲0.1 with a new technique that makes use of nonlinear numerical trajectories and efficient perturbative evolutions to compute waveforms at large radii for the leading and nonleading (ℓ, m) modes. As a proof-of-concept, we compute waveforms for q=1/10. We discuss applications of these techniques for LIGO and VIRGO data analysis and the possibility that our technique can be extended to produce accurate waveform templates from a modest number of fully nonlinear numerical simulations.

Maximum gravitational recoil.

Recent calculations of gravitational radiation recoil generated during black-hole binary mergers have reopened the possibility that a merged binary can be ejected even from the nucleus of a massive host galaxy. Here we report the first systematic study of gravitational recoil of equal-mass binaries with equal, but counteraligned, spins parallel to the orbital plane. Such an orientation of the spins is expected to maximize the recoil. We find that recoil velocity (which is perpendicular to the orbital plane) varies sinusoidally with the angle that the initial spin directions make with the initial linear momenta of each hole and scales up to a maximum of approximately 4000 km s-1 for maximally rotating holes. Our results show that the amplitude of the recoil velocity can depend sensitively on spin orientations of the black holes prior to merger.