Perspective on gravitational self-force analyses

Abstract

A point particle of mass $\mu$ moving on a geodesic creates a perturbation $h_{ab}$, of the spacetime metric $g_{ab}$, that diverges at the particle. Simple expressions are given for the singular $\mu /r$ part of $h_{ab}$ and its distortion caused by the spacetime. This singular part $h^\SS_{ab}$ is described in different coordinate systems and in different gauges. Subtracting $h^\SS_{ab}$ from $h_{ab}$ leaves a regular remainder $h_{ab}^{\mathbb{R}}$. The self-force on the particle from its own gravitational field adjusts the world line at $\Or(μ)$ to be a geodesic of $g_{ab}+h_{ab}^{\mathbb{R}}$; this adjustment includes all of the effects of radiation reaction. For the case that the particle is a small non-rotating black hole, we give a uniformly valid approximation to a solution of the Einstein equations, with a remainder of $\Or(μ^2)$ as $\mu \to 0$. An example presents the actual steps involved in a self-force calculation. Gauge freedom introduces ambiguity in perturbation analysis. However, physically interesting problems avoid this ambiguity.

40 pages, to appear in a special issue of CQG on radiation reaction, contains additional references, improved notation for tensor harmonics

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• Absorption of mass and angular momentum by a black hole: Time-domain formalisms for gravitational perturbations, and the small-hole/slow-motion approximation
• Scalar field self-force effects on orbits about a Schwarzschild black hole
• Reconstruction of Black Hole Metric Perturbations from Weyl Curvature II: The Regge-Wheeler gauge

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