Theoretical Studies in Gravitation and Astrophysics

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The LIGO-VIRGO Scientific Collaboration recently reported the first two direct detections of gravitational wave (GW) signals and demonstrated that these events (named GW150914 and GW151226) were produced by the inspiral and coalescence of binary black holes. This breakthrough marks the beginning of the era of GW astronomy. They also provide the strongest evidence yet that Einstein's theory of general relativity (GR) is the correct theory of gravity and that binary and spinning black holes exist with the properties prescribed by GR. The research funded within this project spans several problems involving GR, the generation of GWs, relativistic hydrodynamics (fluid flow in strong gravitational fields and moving at the speed of light)) and relativistic magnetohydrodynamics (fluid flow in magnetic fields). A common thread uniting the different theoretical topics is the crucial role of gravitation, especially relativistic gravitation. Compact objects (black holes, neutron stars and white dwarfs) provide the principal forum, and the dynamics of matter in a strong gravitational field is a major theme. Some of the topics for investigation include the inspiral and coalescence of compact binaries (binary black holes, binary neutron stars and binary black hole--neutron stars), the generation of GWs from compact binaries and other promising astrophysical sources and the electromagnetic signals that may accompany them (e.g., gamma-ray bursts), gravitational collapse, circumbinary disks around merging supermassive black holes in the cores of galaxies and quasars, and the profile and observable consequences of dark matter (the major form of matter in the universe and unlike normal atoms and their constituents) around supermassive black holes in galaxy cores, including the Milky Way. The results have important implications for astronomical observations, including those planned for GW interferometers, such as the Advanced LIGO/VIRGO network, GEO, KAGRA, the PTAs and LISA, and transient-event electromagnetic detectors, such as the Large Synoptic Survey Telescope (LSST).Most of these topics represent long-standing, fundamental problems in theoretical physics requiring large-scale computation for solution. Hence the approach involves to a significant degree large-scale simulations on supercomputers, in addition to analytical modeling. The key tool will be our robust and well-tested Illinois general relativistic, magnetohydrodynamic (GRMHD) code. The simulations solve Einstein's field equations of GR for gravity coupled to the equations of relativistic MHD for the fluid and Maxwell's equations for the electromagnetic fields. These equations constitute highly nonlinear, coupled partial differential equations in 3+1 dimensions that we solve by finite-differencing. The Illinois GRMHD code employs the BSSN technique with moving puncture gauge conditions to solve the field equations and a high-resolution, shock capturing scheme for the MHD. The problems to be tackled comprise both initial value and evolution computations and treat vacuum spacetimes containing black holes, as well as spacetimes containing realistic matter sources, magnetic fields and both electromagnetic and neutrino radiation ("multimessenger astronomy").