Numerical Hydrodynamics in Strong-Field General Relativity

Abstract

In this thesis we develop and test methods for numerically evolving hydrodynamics coupled to the Einstein field equations, and then apply them to several problems in gravitational physics and astrophysics. The hydrodynamics scheme utilizes high-resolution shock-capturing techniques with flux corrections while the Einstein equations are evolved in the generalized harmonic formulation using finite difference methods. We construct initial data by solving the constraint equations using a multigrid algorithm with free data chosen based on superposing isolated compact objects.

One application we consider is the merger of black hole-neutron star and neutron star-neutron star binaries that form through dynamical capture, as may occur in globular clusters or galactic nuclei. These systems can merge with non-negligible orbital eccentricity and display significant variability in dynamics and outcome as a function of initial impact parameter. We study the electromagnetic and gravitational-wave transients that these mergers may produce and their prospects for being detected with upcoming observations.

We also introduce a numerical technique that allows solutions to the full Einstein equations to be obtained for extreme-mass-ratio systems where the spacetime is dominated by a known background solution. This technique is based on using the knowledge of a background solution to subtract off its contribution to the truncation error. We use this to study the tidal effects and gravitational radiation from a solar-type star falling into a supermassive black hole.

Finally, we utilize general-relativistic hydrodynamics to study ultrarelativistic black hole formation. We study the head-on collision of fluid particles well within the kinetic energy dominated regime (Lorentz factors of 8-12). We find that black hole formation does occur at energies a factor of a few below simple hoop conjecture estimates. We also find that near the threshold for black hole formation, the collision leads to two separate apparent horizons which then merge. Both of these phenomena can be understood in terms of a gravitational focusing effect.