Investigations in Gravitational Wave Sources and Numerical Relativity

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Two problems in gravitational physics will be studied, each of vitalimportance for the current efforts to detect gravitational waves andcharacterize gravitational wave sources. First, gravitational wavesfrom core-collapse supernovae will be analyzed using athree--dimensional computer code based on the Newtonian/quadrupoleapproximation. This work will determine whether dynamical instabilitiessucceed in producing a highly elongated or fragmented inner core, witha correspondingly large gravitational-wave signal. Second, the``Einstein--Christoffel" hyperbolic formulation of general relativitywill be analyzed with particular emphasis on developing a stable,accurate numerical algorithm. Progress will be made toward developing anumerical relativity code that encorporates a high-resolution shockcapturing scheme.Such codes will be needed to investigate the role that gravitationalshocks might play in astrophysical systems. Also, these simulationsconstitute an important step toward determining whether gravitationalwaves from supernovae can be detected by receivers such as LIGO.