Self-force on extreme mass ratio inspirals via curved spacetime effective field theory

TL;DR

This paper develops an effective field theory approach in curved spacetime to compute the self-force on compact objects in extreme mass ratio inspirals, incorporating finite size and tidal effects.

Contribution

It introduces a novel EFT framework for self-force calculations in curved spacetime, including regularization techniques and tidal effects beyond the point particle approximation.

Findings

Derived the first order self-force using EFT methods.

Identified tidal effects at order epsilon^4 affecting inspiral dynamics.

Highlighted potential for tidal disruption of white dwarfs near black holes.

Abstract

In this series we construct an effective field theory (EFT) in curved spacetime to study gravitational radiation and backreaction effects. We begin in this paper with a derivation of the self-force on a compact object moving in the background spacetime of a supermassive black hole. The EFT approach utilizes the disparity between two length scales, which in this problem are the size of the compact object and the radius of curvature of the background spacetime, to treat the orbital dynamics of the compact object, described as an effective point particle, separately from its tidal deformations. Ultraviolet divergences are regularized using Hadamard's {\it partie finie} to isolate the non-local finite part from the quasi-local divergent part. The latter is constructed from a momentum space representation for the graviton retarded propagator and is evaluated using dimensional regularization in which only logarithmic divergences are relevant for renormalizing the parameters of the theory. As a first important application of this framework we explicitly derive the first order self-force given by Mino, Sasaki, Tanaka, Quinn and Wald. Going beyond the point particle approximation, to account for the finite size of the object, we demonstrate that for extreme mass ratio inspirals the motion of a compact object is affected by tidally induced moments at $O(\epsilon^4)$, in the form of an Effacement Principle. The relatively large radius-to-mass ratio of a white dwarf star allows for these effects to be enhanced until the white dwarf becomes tidally disrupted, a potentially $O(\epsilon^2)$ process, or plunges into the supermassive black hole. This work provides a new foundation for further exploration of higher order self force corrections, gravitational radiation and spinning compact objects.