TL;DR
This paper presents a first-principles method for calculating the second-order gravitational self-force on a small body in vacuum spacetime, crucial for modeling extreme mass-ratio inspirals in gravitational-wave astronomy.
Contribution
It provides a novel, gauge-agnostic prescription for computing first and second perturbed metrics and motions using a regular field and effective source approach.
Findings
Derivation of a systematic procedure for second-order self-force calculation
Applicable in any gauge with a sufficiently smooth regular field
Facilitates more accurate modeling of gravitational-wave sources
Abstract
The second-order gravitational self-force on a small body is an important problem for gravitational-wave astronomy of extreme mass-ratio inspirals. We give a first-principles derivation of a prescription for computing the first and second perturbed metric and motion of a small body moving through a vacuum background spacetime. The procedure involves solving for a "regular field" with a specified (sufficiently smooth) "effective source", and may be applied in any gauge that produces a sufficiently smooth regular field.
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