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 mu(< M), it experiences a gravitational self-force whose conservative piece alters the location of the ISCO. Here we calculate the resulting shifts Delta r(isco) and Delta Omega(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(isco)=-3.269(+/- 0.003)mu G/c(2) and Delta Omega(isco)/Omega(isco)=0.4870(+/- 0.0006)mu/M. We discuss the implications of our result within the context of the extreme-mass-ratio binary inspiral problem.