Session Q20 - Gravitational Radiation - Theory and Numerical Relativity.
MIXED session, Monday afternoon, May 01
102A, LBCC
We present approximate analytical solutions to the Hamiltonian and momentum constraint equations, corresponding to systems composed of two black holes with arbitrary linear and angular momentum. The analytical nature of these solutions makes them easier to implement than the traditional numerical approach of solving the corresponding elliptic equations. We show that the methods developed here provide initial data whose violation of the constraint equations falls below the truncation error present in finite difference codes for a given range of grid resolutions. Thus these data are suitable for use in evolutionary codes. In this paper we examine the case of a head-on collision of two mass M black holes at a separation distance of 10M. For this case, we show that the approximate solutions are valid for a range of grid spacings as fine as h = M/8.