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

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.

30 pages, 8 figures

References in corpus (13)

• Phenomenological template family for black-hole coalescence waveforms
• Two timescale analysis of extreme mass ratio inspirals in Kerr. I. Orbital Motion
• The Hyperfine Einstein-Infeld-Hoffmann Potential
• Effective field theory calculation of second post-Newtonian binary dynamics
• Classical Effective Field Theory and Caged Black Holes
• Self-force on extreme mass ratio inspirals via curved spacetime effective field theory
• Second-order gravitational self-force
• Observing white dwarfs orbiting massive black holes in the gravitational wave and electro-magnetic window
• The n-body problem in General Relativity up to the second post-Newtonian order from perturbative field theory
• Construction of the second-order gravitational perturbations produced by a compact object
• A LISA Data-Analysis Primer
• Cosmological Physics with Black Holes (and Possibly White Dwarfs)
• A nonlinear scalar model of extreme mass ratio inspirals in effective field theory II. Scalar perturbations and a master source

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