15th Capra Meeting on Radiation Reaction in General Relativity

Second-order gravitational self-force

Adam Pound

University of Southampton
[SLIDES]

I present a derivation of the second-order gravitational self-force for a small, compact, spherical body. Using the method of matched asymptotic expansions, in a buffer region outside the small body I construct a general solution to the second-order Einstein field equations in the Lorenz gauge, subject only to the condition that the buffer region surrounds the body. This general solution contains all the necessary information, and is sufficiently accurate, to obtain the second-order field globally via a puncture/effective-source scheme. I then find the second-order piece of the force governing the body's motion by matching the general solution to an 'inner expansion' in which the metric takes the form of the small body's spherical spacetime as perturbed by tidal fields.