Linear momentum and gravitational waves: circular orbits around a Schwarzschild black hole

Abstract

Perturbation theory is used to calculate the linear momentum flux in the gravitational waves emitted by a test particle moving on a circular geodesic in the Schwarzschild geometry. Comparisons with previous quasi-Newtonian calculations show good agreement when the radius of the test particle orbit is large and indicate that the quasi-Newtonian approach underestimates the linear momentum flux for smaller orbits. An estimate is made of the recoil velocity induced by a particle plunging into the black hole from the last stable circular orbit.