A practical, covariant puncture for second-order self-force calculations

Abstract

Accurately modeling an extreme-mass-ratio inspiral requires knowledge of the second-order gravitational self-force on the inspiraling small object. Recently, numerical puncture schemes have been formulated to calculate this force, and their essential analytical ingredients have been derived from first principles. However, the \emph{puncture}, a local representation of the small object's self-field, in each of these schemes has been presented only in a local coordinate system centered on the small object, while a numerical implementation will require the puncture in coordinates covering the entire numerical domain. In this paper we provide an explicit covariant self-field as a local expansion in terms of Synge's world function. The self-field is written in the Lorenz gauge, in an arbitrary vacuum background, and in forms suitable for both self-consistent and Gralla-Wald-type representations of the object's trajectory. We illustrate the local expansion's utility by sketching the procedure of constructing from it a numerically practical puncture in any chosen coordinate system.

23 pages, 1 figure, final version to be published in Phys Rev D

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Cited by in corpus (8)

• The Overlap of Numerical Relativity, Perturbation Theory and Post-Newtonian Theory in the Binary Black Hole Problem
• Research Update on Extreme-Mass-Ratio Inspirals
• Tidal invariants for compact binaries on quasi-circular orbits
• Comparison Between Self-Force and Post-Newtonian Dynamics: Beyond Circular Orbits
• Linear-in-mass-ratio contribution to spin precession and tidal invariants in Schwarzschild spacetime at very high post-Newtonian order
• A conservative effect of the second-order gravitational self-force on quasicircular orbits in Schwarzschild spacetime
• Self force on a scalar charge in Kerr spacetime: inclined circular orbits
• Gravitational self-force in nonvacuum spacetimes