Gravitational self-force correction to the innermost stable circular orbit of a Schwarzschild black hole

Abstract

The innermost stable circular orbit (ISCO) of a test particle around a Schwarzschild black hole of mass \(M\) has (areal) radius \(r_{\rm isco}= 6M G/c^2\). If the particle is endowed with mass \(\mu(\ll M)\), it experiences a gravitational self-force whose conservative piece alters the location of the ISCO. Here we calculate the resulting shifts \(\Delta r_{\rm isco}\) and \(\Delta\Omega_{\rm isco}\) in the ISCO's radius and frequency, at leading order in the mass ratio \(\mu/M\). We obtain, in the Lorenz gauge, \(\Delta r_{\rm isco}=-3.269 (\pm 0.003)\mu G/c^2\) and \(\Delta\Omega_{\rm isco}/\Omega_{\rm isco}=0.4870 (\pm 0.0006) \mu/M\). We discuss the implications of our result within the context of the extreme-mass-ratio binary inspiral problem.