Theoretical and Numerical Studies in Gravitational Collapse and Relativistic Astrophysics

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Several theoretical and numerical studies are proposed in gravitational collapse, critical phenomena in general relativity and relativistic astrophysics. The major focuses of this program include: (1) a vigorous investigation of the critical phenomena recently discovered to be associated with gravitational collapse in general relativity, (2) an investigation of several steps toward modeling the orbital decay and coalescence of black hole binaries, (3) several investigations of the physics of eclipsing pulsars and relativistic pulsar winds, and (4) numerical studies of magnetohydrodynamic (MHD) winds and magnetically-confined jets. The objectives of work in critical phenomena are to understand the connections to critical phenomena in other areas such as statistical physics, to explore analytic properties of the simplest examples of critical behavior in collapse, and to discover additional, physically-distinct examples of critical phenomena through numerical experimentation. The objectives of work on coalescing black hole binaries are to develop and explore in two spatial dimensions (2+1) the use of an apparent horizon inner boundary condition for black holes and to develop algorithms that efficiently utilize massively-parallel architectures. In both cases, knowledge developed in 2+1 will be extendible to three dimensions (3+1). Work on eclipsing pulsars will focus on investigating simple analytic/numerical models of nonlinear plasma instabilities, which may be relevant for short-period, low-mass systems, and investigating the interaction between relativistic pulsar winds and normal stellar winds. Continued development of a general purpose MHD code (AVATAR), begun in the last grant period, will be pursued, with application to the study of self-collimation of MHD winds and propagation of magnetically-confined jets.