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arXiv · 2609.08995

Second-order Teukolsky calculations for nonspinning, quasicircular binaries

Benjamin Leather·Andrew Spiers·Adam Pound·Samuel D. Upton·Barry Wardell·Leanne Durkan·Niels Warburton
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Abstract

Currently, the only second-order gravitational self-force calculations have been based on directly solving the perturbative Einstein equations in the Lorenz gauge. That method relied on the complete separability of the Einstein equations in a Schwarzschild background. In this paper, we present a new scheme based on the second-order Teukolsky equation. Crucially, this method promises to extend (reasonably straightforwardly) to the more realistic case of a Kerr background. Here we implement the scheme in the simplest setting of quasicircular orbits around a Schwarzschild black hole. In addition to working with the Teukolsky equation, our scheme incorporates several other advances over previous second-order self-force calculations: compactified hyperboloidal slicing, transformation to a Bondi-Sachs gauge, and a combination of spectral and variation-of-parameters methods. We also use these tools to re-examine the infrared divergences that arise in second-order Lorenz-gauge calculations, showing they are less pronounced in the Teukolsky case and completely eliminated in the Bondi-Sachs gauge. We conclude by calculating the asymptotic energy fluxes and benchmarking them against previous Lorenz-gauge calculations.

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Benjamin Leather, Andrew Spiers, Adam Pound, Samuel D. Upton, Barry Wardell, Leanne Durkan, Niels Warburton. 2026-09-08. Second-order Teukolsky calculations for nonspinning, quasicircular binaries. https://arxiv.org/abs/2609.08995

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