Numerical Simulation of Gravitational Wave Sources and Other Dynamical Spacetimes

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This project will develop mathematical and computational techniques needed to perform computer simulations of realistic astrophysical sources of gravitational radiation: in particular binary black hole and neutron star systems. This research will investigate the following technical problems: 1) pseudo-spectral methods for use in 3D simulations of the binary black hole problem; 2) stability of 3D evolutions in various formulations of the Einstein evolution equations; 3) various methods of constructing astrophysically realistic binary black hole initial data; 4) hyperbolic formulationsof the combined dynamical and gauge evolution equations; 5) tail effects in scalar fields in single black hole spacetimes; 6)variational integration techniques for solving the Einstein evolutionequations; 7) tidal disruption of neutron stars in neutron star/black hole binaries; 8) the dynamics of axisymmetric spacetimes; 9) software development for fully constrained 3D evolution with adaptive mesh refinement; 10) 5D black string spacetimes; 11) and characteristic adaptive mesh refinement code development.The next decade will be an exciting time for gravitational wave (GW) science. During this time the initial LIGO (2002--2006), followed by the advanced LIGO (ca. 2007--2012), and then the LISA (ca. 2011) GW detectors should become operational. These detectors (LIGO in the high-frequency band, 10 to 2000 Hz, and LISA in the low-frequency band, 0.0001 to 0.1 Hz) will become sensitive enough to detect a wide variety of astrophysical GW sources such as binary black hole and neutron star systems, and their observations of these sources will make it possible to do a wide range of new science. Theoretical predictions of the waveforms generated by these sources will be needed for GW searches themselves in some cases, and for extracting the waves' information in all cases. Only by comparing theoretical waveforms with observed ones will it be possible to deducethe nature, structure and dynamics of the source. The strongest and most interesting sources will involve astrophysical systems with strong gravitational fields. These sources are so complex andnonlinear that they can be analyzed only with fully dynamical numerical simulations. This project will develop the mathematical and computational tools that will make it possible to perform the needed simulations of realistic astrophysical gravitational wave sources.