1302.4486 (Chad R. Galley et al.)

Gravitational self-force in the ultra-relativistic limit: The 'large-N'
expansion    [PDF]

Chad R. Galley, Rafael A. Porto

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 with E_m=\gamma m the (kinetic) energy of the small mass. Moreover, we show that diagrams with nonlinear bulk interactions first enter at O(1/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. As an example we derive the self-force to O(\lambda^4/N) and provide expressions for conservative quantities for circular orbits.

View original: http://arxiv.org/abs/1302.4486