HEAD-ON COLLISION OF COMPACT OBJECTS IN GENERAL-RELATIVITY - COMPARISON OF POST-NEWTONIAN AND PERTURBATION APPROACHES

The gravitational-wave energy flux produced during the heed-on infall and collision of two compact objects is calculated using two approache s: (i) a post-Newtonian method, carried to second post-Newtonian order beyond the quadrupole formula, valid for systems of arbitrary masses; and (ii) a black-hole perturbation method, valid for a test body fall ing radially toward a black hole. In the test-body case, the methods a re compared. The post-Newtonian method is shown to converge to the ''e xact'' perturbation result more slowly than expected a priori. A surpr isingly good approximation to the energy radiated during the infall ph ase, as calculated by perturbation theory, is found to be given by a N ewtonian, or quadrupole, approximation combined with the exact test-bo dy equations of motion in the Schwarzschild spacetime.