Dynamical Friction as Environmental Gravitational Self-Force

Abstract

Dynamical friction (DF) and gravitational-wave radiation reaction are conventionally treated as distinct dissipative mechanisms acting on a compact object inspiraling through a matter environment. We show that DF is not an additional force but a term at order $q^2ε$ in a covariant multiparameter expansion of the MiSaTaQuWa force equation that vanishes identically in the absence of a particle-induced perturbation of the environment's matter fields, where $q$ and $ε$ are respectively the mass ratio and environmental parameter. As a test of this identification, we evaluate it in weak and adiabatic field limit, solving the polar density-perturbation equation sourced by the particle's own order-$q$ vacuum metric perturbation. The reduction reproduces the Chandrasekhar-Ostriker drag force and predicts two features in strong gravity. An $\ell$-dependent splitting of the wake that only recombines into the Ostriker source in the weak-field limit, and a purely relativistic axial contribution with no Newtonian counterpart. This establishes dynamical friction as an intrinsic piece of self-force theory, extending to strong field, generic orbits, and generic environments, with direct consequences for extreme-mass-ratio inspiral waveform modeling for LISA.