Gravitational self-force in the ultra-relativistic limit: The 'large-N'
  expansion
  We study the gravitational self-force using the effective field theory
formalism. We show that in the ultra-relativistic limit \gamma \to \infty, with
\gamma the boost factor, many simplifications arise. Drawing parallels with the
large N limit in quantum field theory, we introduce the parameter 1/N =
1/\gamma^2 and show that the effective action admits a well defined expansion
in powers of \lambda = N\epsilon, at each order in 1/N, where \epsilon = E_m/M
and E_m=\gamma m is the (kinetic) energy of the small mass. Moreover, we show
that diagrams with nonlinear bulk interactions first enter at O(\lambda^2/N^2)
and only diagrams with nonlinearities in the worldline couplings, which are
significantly easier to compute, survive in the large N/ultra-relativistic
limit. Finally, we derive the self-force to O(\lambda^4/N) and provide
expressions for some conservative quantities for circular orbits.
