Gravitational Self-Force Correction to the Innermost Stable Circular Orbit of a Schwarzschild Black Hole

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