Theoretical and numerical studies will be initiated for an array of problems in gravitational physics and relativistic astrophysics. Topics of interest include (1) development of techniques in numerical relativity and their application in modeling sources of gravitational radiation and in exploring nonlinear, dynamical spacetimes; (2) numerical modeling of the tidal disruption of stars during close encounters with massive black holes and the possible relevance of disruption for feeding active galactic nuclei; (3) the calculation of magnetohydrodynamic (MHD) winds from accretion disks and stars and the development of a general relativistic MHD numerical scheme; and (4) a study of the recently discovered eclipsing millisecond pulsar 1957+20. The goal of this work is to acquire a deeper understanding of self-gravitating and dynamical systems and of high energy (relativistic) phenomena. Many of these physical studies rely upon the use of large-scale numerical modeling techniques. Accordingly, useful byproducts of such studies are almost invariably new and refined numerical algorithms. The project relating to the eclipsing pulsar 1957+20 is of a more phenomenological nature and relies upon the close interplay between theoretical calculation and observational evidence.
