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A nonlinear scalar model of extreme mass ratio inspirals in effective field theory: II. Scalar perturbations and a master source

Galley, Chad R. (2012) A nonlinear scalar model of extreme mass ratio inspirals in effective field theory: II. Scalar perturbations and a master source. Classical and Quantum Gravity, 29 (1). Art. No. 015011. ISSN 0264-9381.

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The motion of a small compact object (SCO) in a background spacetime is investigated further in the context of a class of model nonlinear scalar field theories that have a perturbative structure analogous to the general relativistic description of extreme mass ratio inspirals. We derive regular expressions for the scalar perturbations generated by the motion of the compact object that are valid through third order in ε the size of the SCO to the background curvature length scale. Our results for the field perturbations are compared to those calculated through second order in ε by Rosenthal (2005 Class. Quantum Grav. 22 S859) and found to agree. However, our procedure for regularizing the scalar perturbations is considerably simpler. Following the Detweiler–Whiting scheme, we use our results for the regular expressions for the field and derive the regular self-force corrections through third order. We find agreement with our previous derivation based on a variational principle of an effective action for the worldline associated with the SCO thereby demonstrating the internal consistency of our formalism. This also explicitly demonstrates that the Detweiler–Whiting decomposition of Green’s functions is a valid and practical method of self-force computation at higher orders in perturbation theory and more generally, at all orders in perturbation theory, as we show in an appendix. Finally, we identify a central quantity, which we call a master source, from which all other physically relevant quantities are derivable. Specifically, knowing the master source through some order in ε allows one to construct the waveform measured by an observer, the regular part of the field and its derivative on the worldline, the regular part of the self-force and various orbital quantities such as shifts of the innermost stable circular orbit, etc when restricting to conservative dynamics. The existence of a master source together with the regularization methods implemented in this series should be indispensable for derivations of higher order gravitational self-force corrections in the future.

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Additional Information:© 2012 IOP Publishing Ltd. Received 29 September 2011. Published 13 December 2011. We thank Tanja Hinderer for providing valuable feedback and comments on a previous draft. This work was supported in part by an appointment to the NASA Postdoctoral Program at the Jet Propulsion Laboratory administered by Oak Ridge Associated Universities through a contract with NASA.
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NASA Postdoctoral Program at JPLUNSPECIFIED
Issue or Number:1
Classification Code:PACS: 11.10.Lm; 11.10.Gh; 04.20.Fy; 04.62.+v; 04.20.Gz. MSC: 83C75; 81T15
Record Number:CaltechAUTHORS:20120124-105917848
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Official Citation: A nonlinear scalar model of extreme mass ratio inspirals in effective field theory: II. Scalar perturbations and a master source Chad R Galley 2012 Class. Quantum Grav. 29 015011
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:28936
Deposited By: Ruth Sustaita
Deposited On:24 Jan 2012 19:18
Last Modified:03 Oct 2019 03:36

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