A nonlinear scalar model of extreme mass ratio inspirals in effective field theory I. Self force through third order

TL;DR

This paper develops a nonlinear scalar field model to study the self force on a small compact object in extreme mass ratio inspirals, applying effective field theory up to third order to facilitate higher-order calculations.

Contribution

It introduces a simplified nonlinear scalar model for EMRIs and demonstrates the calculation of the self force up to third order using effective field theory and renormalization techniques.

Findings

Self force calculated through third order in the model.

Formalism ensures finiteness of the self force at higher orders.

Model provides a simpler context for studying higher-order self force effects.

Abstract

The motion of a small compact object in a background spacetime is investigated in the context of a model nonlinear scalar field theory. This model is constructed to have a perturbative structure analogous to the General Relativistic description of extreme mass ratio inspirals (EMRIs). We apply the effective field theory approach to this model and calculate the finite part of the self force on the small compact object through third order in the ratio of the size of the compact object to the curvature scale of the background (e.g., black hole) spacetime. We use well-known renormalization methods and demonstrate the consistency of the formalism in rendering the self force finite at higher orders within a point particle prescription for the small compact object. This nonlinear scalar model should be useful for studying various aspects of higher-order self force effects in EMRIs but within a comparatively simpler context than the full gravitational case. These aspects include developing practical schemes for higher order self force numerical computations, quantifying the effects of transient resonances on EMRI waveforms and accurately modeling the small compact object's motion for precise determinations of the parameters of detected EMRI sources.