Abstract:
We use simulations of hydrodynamics coupled with full general relativity to investigate the gravitational waves produced by a star colliding with a massive black hole when the star's tidal disruption radius lies far outside of the black hole horizon. We consider both main-sequence and white-dwarf compaction stars, and nonspinning black holes, as well as those with near-extremal spin. We study the regime in between where the star can be accurately modeled by a point particle, and where tidal effects completely suppress the gravitational wave signal. We find that nonnegligible gravitational waves can be produced even when the star is strongly affected by tidal forces, as well as when it collides with large angular momentum. We discuss the implications that these results have for the potential observation of gravitational waves from these sources with future detectors.

Abstract:
We introduce a new method for numerically evolving the full Einstein field equations in situations where the spacetime is dominated by a known background solution. The technique leverages the knowledge of the background solution to subtract off its contribution to the truncation error, thereby more efficiently achieving a desired level of accuracy. We demonstrate the method by applying it to the radial infall of a solar-type star into supermassive black holes with mass ratios $\geq 10^6$. The self-gravity of the star is thus consistently modeled within the context of general relativity, and the star's interaction with the black hole computed with moderate computational cost, despite the over five orders of magnitude difference in gravitational potential (as defined by the ratio of mass to radius). We compute the tidal deformation of the star during infall, and the gravitational wave emission, finding the latter is close to the prediction of the point-particle limit.

Abstract:
Freely decaying relativistic force-free turbulence is studied for the first time. We initiate the magnetic field at a short wavelength and simulate its relaxation toward equilibrium on two and three dimensional periodic domains, in both helical and non-helical settings. Force-free turbulent relaxation is found to exhibit an inverse cascade in all settings, and in 3D to have a magnetic energy spectrum consistent with the Kolmogorov $5/3$ power law. 3D relaxations also obey the Taylor hypothesis; they settle promptly into the lowest energy configuration allowed by conservation of the total magnetic helicity. But in 2D, the relaxed state is a force-free equilibrium whose energy greatly exceeds the Taylor minimum, and which contains persistent force-free current layers and isolated flux tubes. We explain this behavior in terms of additional topological invariants that exist only in two dimensions, namely the helicity enclosed within each level surface of the magnetic potential function. The speed and completeness of turbulent magnetic free energy discharge could help account for rapidly variable gamma-ray emission from the Crab Nebula, gamma-ray bursts, blazars, and radio galaxies.

Abstract:
Freely decaying relativistic force-free turbulence is studied for the first time. We initiate the magnetic field at a short wavelength and simulate its relaxation toward equilibrium on two and three dimensional periodic domains, in both helical and non-helical settings. Force-free turbulent relaxation is found to exhibit an inverse cascade in all settings, and in 3D to have a magnetic energy spectrum consistent with the Kolmogorov $5/3$ power law. 3D relaxations also obey the Taylor hypothesis; they settle promptly into the lowest energy configuration allowed by conservation of the total magnetic helicity. But in 2D, the relaxed state is a force-free equilibrium whose energy greatly exceeds the Taylor minimum, and which contains persistent force-free current layers and isolated flux tubes. We explain this behavior in terms of additional topological invariants that exist only in two dimensions, namely the helicity enclosed within each level surface of the magnetic potential function. The speed and completeness of turbulent magnetic free energy discharge could help account for rapidly variable gamma-ray emission from the Crab Nebula, gamma-ray bursts, blazars, and radio galaxies.

Abstract:
We study dynamical capture binary neutron star mergers as may arise in dense stellar regions such as globular clusters. Using general-relativistic hydrodynamics, we find that these mergers can result in the prompt collapse to a black hole or in the formation of a hypermassive neutron star, depending not only on the neutron star equation of state but also on impact parameter. We also find that these mergers can produce accretion disks of up to a tenth of a solar mass and unbound ejected material of up to a few percent of a solar mass. We comment on the gravitational radiation and electromagnetic transients that these sources may produce.

Abstract:
We study the ultrarelativistic head-on collision of equal mass particles, modeled as self-gravitating fluid spheres, by numerically solving the coupled Einstein-hydrodynamic equations. We focus on cases well within the kinetic energy dominated regime, where between 88-92% ($\gamma=8$ to 12) of the initial net energy of the spacetime resides in the translation kinetic energy of the particles. We find that for sufficiently large boosts, black hole formation occurs. Moreover, near yet above the threshold of black hole formation, the collision initially leads to the formation of two distinct apparent horizons that subsequently merge. We argue that this can be understood in terms of a focusing effect, where one boosted particle acts as a gravitational lens on the other and vice versa, and that this is further responsible for the threshold being lower (by a factor of a few) compared to simple hoop conjecture estimates. Cases slightly below threshold result in complete disruption of the model particles. The gravitational radiation emitted when black holes form reaches luminosities of 0.014 $c^5/G$, carrying $16\pm2%$ of the total energy.

Abstract:
We study dynamical capture binary black hole-neutron star (BH-NS) mergers focusing on the effects of the neutron star spin. These events may arise in dense stellar regions, such as globular clusters, where the majority of neutron stars are expected to be rapidly rotating. We initialize the BH-NS systems with positions and velocities corresponding to marginally unbound Newtonian orbits, and evolve them using general-relativistic hydrodynamical simulations. We find that even moderate spins can significantly increase the amount of mass in unbound material. In some of the more extreme cases, there can be up to a third of a solar mass in unbound matter. Similarly, large amounts of tidally stripped material can remain bound and eventually accrete onto the BH---as much as a tenth of a solar mass in some cases. These simulations demonstrate that it is important to treat neutron star spin in order to make reliable predictions of the gravitational wave and electromagnetic transient signals accompanying these sources.

Abstract:
There is a high level of interest in black hole-neutron star binaries, not only because their mergers may be detected by gravitational wave observatories in the coming years, but also because of the possibility that they could explain a class of short duration gamma-ray bursts. We study black hole-neutron star mergers that occur with high eccentricity as may arise from dynamical capture in dense stellar regions such as nuclear or globular clusters. We perform general relativistic simulations of binaries with a range of impact parameters, three different initial black hole spins (zero, aligned and anti-aligned with the orbital angular momentum), and neutron stars with three different equations of state. We find a rich diversity across these parameters in the resulting gravitational wave signals and matter dynamics, which should also be reflected in the consequent electromagnetic emission. Before tidal disruption, the gravitational wave emission is significantly larger than perturbative predictions suggest for periapsis distances close to effective innermost stable separations, exhibiting features reflecting the zoom-whirl dynamics of the orbit there. Guided by the simulations, we develop a simple model for the change in orbital parameters of the binary during close encounters. Depending upon the initial parameters of the system, we find that mass transfer during non-merging close encounters can range from essentially zero to a sizable fraction of the initial neutron star mass. The same holds for the amount of material outside the black hole post-merger, and in some cases roughly half of this material is estimated to be unbound. We also see that non-merging close encounters generically excite large oscillations in the neutron star that are qualitatively consistent with f-modes.

Abstract:
In order to understand the conditions which lead a highly magnetized, relativistic plasma to become unstable, and in such cases how the plasma evolves, we study a prototypical class of magnetostatic equilibria where the magnetic field satisfies $\nabla \times\mathbf B = \alpha \mathbf B$, where $\alpha$ is spatially uniform, on a periodic domain. Using numerical solutions we show that generic examples of such equilibria are unstable to ideal modes (including incompressible ones) which are marked by exponential growth in the linear phase. We characterize the unstable mode, showing how it can be understood in terms of merging magnetic and current structures, and explicitly demonstrate its instability using the energy principle. Following the nonlinear evolution of these solutions, we find that they rapidly develop regions with relativistic velocities and electric fields of comparable magnitude to the magnetic field, liberating magnetic energy on dynamical timescales and eventually settling into a configuration with the largest allowable wavelength. These properties make such solutions a promising setting for exploring the mechanisms behind extreme cosmic sources of gamma rays.

Abstract:
We study the superradiant scattering of gravitational waves by a nearly extremal black hole (dimensionless spin $a=0.99$) by numerically solving the full Einstein field equations, thus including backreaction effects. This allows us to study the dynamics of the black hole as it loses energy and angular momentum during the scattering process. To explore the nonlinear phase of the interaction, we consider gravitational wave packets with initial energies up to $10%$ of the mass of the black hole. We find that as the incident wave energy increases, the amplification of the scattered waves, as well as the energy extraction efficiency from the black hole, is reduced. During the interaction the apparent horizon geometry undergoes sizable nonaxisymmetric oscillations. The largest amplitude excitations occur when the peak frequency of the incident wave packet is above where superradiance occurs, but close to the dominant quasinormal mode frequency of the black hole.