Edward Y. M. Wang

Coordinate conditions in three-dimensional numerical relativity

We put forward a few ideas on coordinate (gauge) conditions in numerical relativity. Coordinate conditions are important for long time scale simulations of relativistic systems. We demonstrate the importance of, and propose methods for, the active enforcement of coordinate properties. In particular, the constancy of the determinant of the spatial 3-metric is investigated as such a property. We propose an exceedingly simple but powerful idea for implementing elliptic coordinate conditions that not only makes possible the use of complicated elliptic conditions, but is also a number of orders of magnitude more efficient than existing methods for large-scale three-dimensional simulations.

Numerical Models of Binary Neutron Star System Mergers. II. Coalescing Models with Post-Newtonian Radiation Reaction Forces

Using a grid-based staggered-mesh hydrodynamics code, we present the evolution of initially Newtonian equilibrium configurations of symmetric binary neutron star systems under the influence of a post-Newtonian gravitational radiation reaction potential. These simulations indicate that the time to merger for binaries with separations on the order of a few stellar radii is between and 1 Keplerian period of the initial configuration. These results are in contrast to the larger timescales calculated from earlier smoothed particle hydrodynamics calculations that include quadrupolar-type radiation reaction forces. The implications of our studies are discussed in the context of observable effects on the gravitational waveforms expected to be observed by ground-based gravity-wave detectors such as the Laser Interferometer Gravitational-Wave Observatory and the restrictions placed on the choice of initial data for fully relativistic calculations.

Coalescing binary neutron star systems

We present numerical studies of coalescing neutron star pairs with Newtonian hydrodynamics coupled to the 2.5 Post-Newtonian radiation reaction of Blanchet, Damour, and Schafer [1]. Our simulations evolve the Euler equations using a modification of the ZEUS 2-D algorithm [2] and use a Fast Fourier Transformation method for solving the Poisson equation for the gravitational and radiation reaction potentials. We find that the radiation reaction produces a significant effect on a neutron star pair when compared to a purely Newtonian simulation.