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 r₈ₒ₂₎=6MG/c^2. If the particle is endowed with mass (), it experiences a gravitational self-force whose conservative piece alters the location of the ISCO. Here we calculate the resulting shifts r₈ₒ₂₎ and ₈ₒ₂₎ in the ISCO's radius and frequency, at leading order in the mass ratio /M. We obtain, in the Lorenz gauge, r₈ₒ₂₎=-3. 269 (0. 003) /c^2 and ₈ₒ₂₎/₈ₒ₂₎=0. 4870 (0. 0006) /M. We discuss the implications of our result within the context of the extreme-mass-ratio binary inspiral problem.