Gravitational self force in extreme mass-ratio inspirals

TL;DR

This review discusses recent theoretical and computational advances in calculating the gravitational self-force on particles orbiting black holes, crucial for gravitational wave detection from extreme mass-ratio inspirals.

Contribution

It provides a comprehensive survey of methods for computing the gravitational self-force, including detailed analysis of mode-sum and m-mode regularization techniques in Kerr spacetime.

Findings

Development of practical computational frameworks for self-force calculations.

Implementation of mode-sum method for eccentric orbits in Schwarzschild spacetime.

Derivation of regularization parameters for Kerr spacetime.

Abstract

This review is concerned with the gravitational self-force acting on a mass particle in orbit around a large black hole. Renewed interest in this old problem is driven by the prospects of detecting gravitational waves from strongly gravitating binaries with extreme mass ratios. We begin here with a summary of recent advances in the theory of gravitational self-interaction in curved spacetime, and proceed to survey some of the ideas and computational strategies devised for implementing this theory in the case of a particle orbiting a Kerr black hole. We review in detail two of these methods: (i) the standard mode-sum method, in which the metric perturbation is regularized mode-by-mode in a multipole decomposition, and (ii) $m$-mode regularization, whereby individual azimuthal modes of the metric perturbation are regularized in 2+1 dimensions. We discuss several practical issues that arise, including the choice of gauge, the numerical representation of the particle singularity, and how high-frequency contributions near the particle are dealt with in frequency-domain calculations. As an example of a full end-to-end implementation of the mode-sum method, we discuss the computation of the gravitational self-force for eccentric geodesic orbits in Schwarzschild, using a direct integration of the Lorenz-gauge perturbation equations in the time domain. With the computational framework now in place, researchers have recently turned to explore the physical consequences of the gravitational self force; we will describe some preliminary results in this area. An appendix to this review presents, for the first time, a detailed derivation of the regularization parameters necessary for implementing the mode-sum method in Kerr spacetime.