Title: 'Bartnik's splitting conjecture and results in its favor'
Abstract: Singularity theorems suggest that many spacetimes are geodesically incomplete. One way to test this idea is to show that geodesically complete spacetimes have to be special in some sense. In 1982 Yau conjectured a statement of this kind (which was proven in the 80s) and in 1988 Bartnik made the stronger and still open conjecture that spacetimes with compact Cauchy surfaces that satisfy the strongenergy condition must be static. Bartnik's conjecture turns out to be implied by an even stronger conjecture that such spacetimes actually admit Constant Mean Curvature Cauchy surfaces. Some results in support of these conjectures will be described.
Title: Simulating and Imaging Supermassive Black Hole Accretion Flows
Abstract: Supermassive black holes exist at the hearts of nearly all galaxies. They are most frequently surrounded by hot, thick, and low-radiative-efficiency accretion flows, including in the Galactic Center radio source Sagittarius A* (Sgr A*) and at the base of the relativistic jet in the giant galaxy M87. In this thesis, I study these objects in two ways: in numerical simulations and with image reconstruction of data from the Event Horizon Telescope (EHT), a mm-wavelength Very Long Baseline Interferometry (VLBI) array. In the first part, I simulate both Sgr A* and M87 using two-temperature, radiative general relativistic magnetohydrodynamics (GRMHD). As electrons and ions in hot flows are far from mutual equilibrium, including radiation and thermodynamics in these simulations is necessary to predict the electron temperatures and emission from these objects and connect observations to the underlying plasma microphysics operating in these systems. In the second part, I describe a framework for imaging VLBI data with regularized maximum likelihood methods, implemented in the eht-imaging software library. This framework allows VLBI data to be imaged with no a priori calibration, using only robust closure quantities. Finally, I present images from the first full EHT campaign on M87 reconstructed using eht-imaging and other methods and describe measurements of the black hole shadow and mass from these first images of a supermassive black hole.