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 risco=6MG/c2. If the particle is endowed with mass μ(μM), it experiences a gravitational self-force whose conservative piece alters the location of the ISCO. Here we calculate the resulting shifts Δrisco and ΔΩisco in the ISCO's radius and frequency, at leading order in the mass ratio μ/M. We obtain, in the Lorenz gauge, Δrisco=-3.269(±0.003)μG/c2 and ΔΩisco/Ωisco=0.4870(±0.0006)μ/M. We discuss the implications of our result within the context of the extreme-mass-ratio binary inspiral problem.