Orbital evolution of a test particle around a black hole: Higher-order corrections

We study under certain assumptions the orbital evolution of a radiation-damped binary in the extreme mass ratio limit, and the resulting waveforms, to one order beyond what can be obtained using the conservation laws approach. The equations of motion are solved perturbatively in the mass ratio (or the corresponding parameter in the scalar field toy model), using the self-force, for quasicircular orbits around a Schwarzschild black hole. This approach is applied for the scalar model. Higher-order corrections yield a phase shift which, if included, may make gravitational-wave astronomy potentially highly accurate.