1209.0964 (Sarp Akcay et al.)

Gravitational self-force and the effective-one-body formalism between
the innermost stable circular orbit and the light ring    [PDF]

Sarp Akcay, Leor Barack, Thibault Damour, Norichika Sago

We compute the conservative piece of the gravitational self-force (GSF) acting on a particle of mass $m_1$ as it moves along an (unstable) circular geodesic orbit between the innermost stable circular orbit (ISCO) and the light ring of a Schwarzschild black hole of mass $m_2\gg m_1$. More precisely, we construct the function $h_{uu}(x) \equiv h_{\mu\nu} u^{\mu} u^{\nu}$ (related to Detweiler's gauge-invariant "redshift" variable), where $h_{\mu\nu}$ is the regularized metric perturbation in the Lorenz gauge, $u^{\mu}$ is the four-velocity of $m_1$, and $x\equiv [Gc^{-3}(m_1+m_2)\Omega]^{2/3}$ is an invariant coordinate constructed from the orbital frequency $\Omega$. In particular, we explore the behavior of $h_{uu}$ just outside the "light ring" at $x=1/3$, where the circular orbit becomes null. Using the recently discovered link between $h_{uu}$ and the piece $a(u)$, linear in the symmetric mass ratio $nu$, of the main radial potential $A(u,\nu)$ of the Effective One Body (EOB) formalism, we compute $a(u)$ over the entire domain $0View original: http://arxiv.org/abs/1209.0964