Nonlinearly self-interacting extended bodies move as test bodies in effective external fields

2025/04/16 by Abraham I. Harte, Harte, Abraham I., Francisco M. Blanco +3 · 3 citations
Materials Science · Physics and Astronomy · #Equations of motion #FOS: Physical sciences #Formalism (music) #General Relativity and Quantum Cosmology (gr-qc) #Gravitational field #Nonlinear system #Nonlocal and gradient elasticity in micro/nano structures #Pulsars and Gravitational Waves Research #Quantum and Classical Electrodynamics #Regularization (linguistics) #Scalar (mathematics) #Scalar field

paper · pdf · doi:10.48550/arxiv.2504.11912

published in arXiv (Cornell University) (Cornell University)

openalex publication_date 2025/04/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

In electromagnetism, linearized general relativity, and other contexts, previous work has shown that the laws of motion which govern compact, self-interacting bodies can be obtained by applying "Detweiler-Whiting prescriptions" to the laws of motion which govern test bodies. These prescriptions replace any field which appears in a test-body law of motion with a certain effective field which is a quasilocal functional of the physical variables -- a functional that can be interpreted as a regularization procedure in a point-particle limit. We generalize these results, presenting a formalism which allows Detweiler-Whiting prescriptions to be be directly derived for extended bodies, even in nonlinear field theories. If a generating functional with particular properties can be constructed, we find effective linear and angular momenta which evolve via Mathisson-Papapetrou-Dixon equations involving appropriate effective fields. These equations implicitly incorporate all self-force, self-torque, and extended-body effects. Although our main focus is on bodies coupled to nonlinear scalar fields, we also remark on the gravitational case.

Citations

• Second-order gravitational self-force in a highly regular gauge
• Self-force and radiation reaction in general relativity
• Foundations of the self-force problem in arbitrary dimensions
• Nonlinear gravitational self-force: second-order equation of motion
• Self-forces on static bodies in arbitrary dimensions
• Center of mass, spin supplementary conditions, and the momentum of spinning particles
• Motion in classical field theories and the foundations of the self-force problem
• Second-order gravitational self-force
• A nonlinear scalar model of extreme mass ratio inspirals in effective field theory II. Scalar perturbations and a master source
• Mechanics of extended masses in general relativity
• On the center of mass in general relativity
• A nonlinear scalar model of extreme mass ratio inspirals in effective field theory I. Self force through third order
• Effective stress-energy tensors, self-force, and broken symmetry
• A Rigorous Derivation of Electromagnetic Self-force
• Electromagnetic self-forces and generalized Killing fields
• Self-forces from generalized Killing fields
• Approximate spacetime symmetries and conservation laws
• The motion of point particles in curved spacetime
• The motion of point particles in curved spacetime
• Self-force via a Green’s function decomposition
• Dynamics of extended bodies in general relativity III. Equations of motion

Cited by

• The Magnusian generator for dissipative systems and application to leading 2.5PN radiation-reaction dynamics
• Effective source for second-order self-force calculations: quasicircular orbits in Schwarzschild spacetime
• Constants of motion in gravitational self-force theory

Related

• Effects of the singular self-field on the motion of an extended body
• Self-forces from generalized Killing fields
• Extended-body approach to the electromagnetic self-force in curved spacetime
• Generalized Papapetrou's equations of motion for an extended test body within static and isotropic metrics
• The Self-Force Problem: Local Behaviour of the Detweiler-Whiting Singular Field