Gravitational wave trains in the quasiequilibrium approximation: A model problem in scalar gravitation - art. no. 064035

A quasiequilibrium (QE) computational scheme was recently developed in gene ral relativity to calculate the complete gravitational wave train emitted d uring the inspiral phase of compact binaries. The QE method exploits the fa ct that the gravitational radiation inspiral time scale is much longer than the orbital period everywhere outside the ISCO. Here we demonstrate the va lidity and advantages of the QE scheme by solving a model problem in relati vistic scaler gravitation theory. By adopting scalar gravitation, we an abl e td numerically track without approximation the damping of a simple, quasi periodic radiating system tan oscillating spherical matter shell) to final equilibrium, and then use the exact numerical results to calibrate the QE a pproximation method. In particular, we calculate the emitted gravitational wave train three different ways: by integrating the exact coupled dynamical field and matter equations, by using the scalar-wave monopole approximatio n formula (corresponding to the quadrupole formula in general relativity), and by adopting the QE scheme. We find that the monopole formula works well for weak field cases, but fails when the fields become even moderately str ong. By contrast, the QE scheme remains quite reliable for moderately stron g fields, and begins to breakdown only for ultrastrong fields. The QE schem e thus provides a promising technique to construct the complete wave train from binary inspirer outside the ISCO, when the gravitational fields are st rong, but when the computational resources required to follow the system fo r more than a few orbits by direct numerical integration of the exact equat ions are prohibitive.