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Gravitational self-force in the ultra-relativistic limit: the "large-N" expansion

Galley, Chad R. and Porto, Rafael A. (2013) Gravitational self-force in the ultra-relativistic limit: the "large-N" expansion. Journal of High Energy Physics, 2013 (11). Art. No. 96. ISSN 1126-6708.

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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 O (λ^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 (λ^4/N) and provide expressions for some conservative quantities for circular orbits.

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Additional Information:© 2013 SISSA. Published for SISSA by Springer. Received: September 25, 2013. Accepted: October 18, 2013. Published: November 12, 2013. We thank Alexandre Le Tiec for helpful discussions and the organizers and participants of the workshop "Chirps, Mergers, and Explosions: The Final Moments of Coalescing Binaries" held at the KITP where this work originated (NSF Grant No. PHY05-25915). C.R.G. was supported by NSF grant PHY-1068881 and CAREER grant PHY-0956189; R.A.P. was supported by NSF grant AST-0807444 and DOE grant DE-FG02-90ER40542.
Funding AgencyGrant Number
Department of Energy (DOE)DE-FG02-90ER40542
Subject Keywords:Classical Theories of Gravity, Black Holes
Issue or Number:11
Record Number:CaltechAUTHORS:20130305-143738143
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Official Citation: Gravitational self-force in the ultra-relativistic limit: the “large-N ” expansion Chad R. Galley, Rafael A. Porto Article:96
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:37315
Deposited By: JoAnn Boyd
Deposited On:27 Mar 2013 18:07
Last Modified:03 Oct 2019 04:46

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