Abstract
We study the gravitational self-force using the effective field theory formalism. We show that in the ultra-relativistic limit γ → ∞, with γ the boost factor, many simplifications arise. Drawing parallels with the large N limit in quantum field theory, we introduce the parameter 1/N ≡ 1/γ 2 and show that the effective action admits a well defined expansion in powers of λ ≡ N ϵ at each order in 1/N , where ϵ ≡ E m /M and E m = γm is the (kinetic) energy of the small mass. Moreover, we show that diagrams with nonlinear bulk interactions first enter at \( \mathcal{O} \)(λ2 /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 \( \mathcal{O} \)(λ4 /N) and provide expressions for some conservative quantities for circular orbits.
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Galley, C.R., Porto, R.A. Gravitational self-force in the ultra-relativistic limit: the “large-N ” expansion. J. High Energ. Phys. 2013, 96 (2013). https://doi.org/10.1007/JHEP11(2013)096
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DOI: https://doi.org/10.1007/JHEP11(2013)096