[0902.0573] Gravitational self-force correction to the innermost stable circular orbit of a Schwarzschild black hole

Authors: Leor Barack, Norichika Sago

Date: 3 Feb 2009

Abstract: The innermost stable circular orbit (ISCO) of a test particle around a Schwarzschild black hole of mass $M$ is located at $r_{\rm isco}=6M G/cˆ2$ (Schwarzschild coordinate radius). 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 $\Delta r_{\rm isco}=-3.27 \mu G/cˆ2$ (in the Lorenz gauge) and $\Delta\Omega_{\rm isco}/\Omega_{\rm isco}=0.487 \mu/M$ (gauge invariant). We discuss the implications of our result within the context of extreme mass-ratio binary inspirals.

Feb 06, 2009

0902.0573 (/preprints)
2009-02-06, 09:15