Gravity seminar - Sam Dolan Seminar

The Gravitational Self-Force (GSF) formalism, a natural extension of black hole perturbation theory, has been developed to compute physical effects in binary systems with large mass ratios, m << M. The first-order GSF approach yields a regularized metric perturbation and its first derivatives, which in principle harbours all physical content at O(m/M), and also a great deal of gauge freedom. A key question is: what are the `conservative' gauge-invariant physical effects at O(m/M) arising from GSF calculations which can be compared with other approaches, such as Post-Newtonian expansions, Numerical Relativity and Effective One-Body theory? In 2008, Detweiler identified two related effects for (quasi-)circular orbits: O(m/M) shifts in the orbital frequency and a redshift invariant. This led on to computations by Barack and collaborators of shifts in the frequency of the innermost stable circular orbit, and periastron advance in eccentric orbits, which became key points of comparison.

In this talk, I will describe recent work in collaboration with Harte, Le Tiec, Warburton and Barack. I will argue that there is an additional effect for quasi-circular orbits at O(m/M) that has been overlooked, related to the free precession of a spin vector parallel-transported around the circle. The key result is a shift in the precession frequency at O(m/M) that is gauge-invariant. I will present a comparison between the results of a GSF calculation, and a new Post-Newtonian expansion. I will discuss the scope for future calculations of self-force effects on geodetic precession in binaries.