Frequency-domain extended-effective-source gravitational self-force for eccentric Schwarzschild orbits
Abstract
Effective-source formulations provide a practical route to gravitational self-force (GSF) calculations when singular retarded fields cannot be handled directly mode by mode. Up to now, only frequency-domain first-order GSF for circular orbits in Schwarzschild spacetime was obtained with the effective-source method. We construct and implement a frequency-domain extended effective-source (EES) formulation for first-order Lorenz-gauge GSF on eccentric orbits in Schwarzschild spacetime. The central obstacle is that radial libration forces the physical puncture and effective source to switch between interior and exterior branches, limiting their differentiability and producing slow spectral convergence. We overcome this obstruction by analytically extending both branches across the libration region and solving the coupled Lorenz-gauge perturbation equations for the resulting smooth extended sources. This provides an end-to-end gravitational EES implementation for eccentric motion and validates a computational ingredient needed for extending frequency-domain effective-source calculations toward second order.
Related
- Gravitational waves away from a Schwarzschild black hole: full spectrum analysis
- Analytic Electromagnetic Effective Source for Geodesic Orbit in Schwarzschild Spacetime
- Gravitational wave signatures of periodic orbits around a Schwarzschild-like black hole
- Efficient Eccentric Effective-One-Body Dynamics via Near-Identity Averaging Transformations
- Efficient Eccentric and Quasicircular Effective-One-Body Waveforms via Near-Identity Averaging Transformations
BibTeX
@misc{lu2026frequencydomain,
title = {{Frequency-domain extended-effective-source gravitational self-force for eccentric Schwarzschild orbits}},
author = {Xuchen Lu and Yungui Gong and Bokai Zhang and Chao Zhang and Wenting Zhou},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.02635},
eprint = {2609.02635},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.02635},
}
RIS
TY - UNPB
TI - Frequency-domain extended-effective-source gravitational self-force for eccentric Schwarzschild orbits
AU - Xuchen Lu
AU - Yungui Gong
AU - Bokai Zhang
AU - Chao Zhang
AU - Wenting Zhou
PY - 2026
DA - 2026/09/02
PB - arXiv
DO - 10.48550/arxiv.2609.02635
UR - https://arxiv.org/abs/2609.02635
AB - Effective-source formulations provide a practical route to gravitational self-force (GSF) calculations when singular retarded fields cannot be handled directly mode by mode. Up to now, only frequency-domain first-order GSF for circular orbits in Schwarzschild spacetime was obtained with the effective-source method. We construct and implement a frequency-domain extended effective-source (EES) formulation for first-order Lorenz-gauge GSF on eccentric orbits in Schwarzschild spacetime. The central obstacle is that radial libration forces the physical puncture and effective source to switch between interior and exterior branches, limiting their differentiability and producing slow spectral convergence. We overcome this obstruction by analytically extending both branches across the libration region and solving the coupled Lorenz-gauge perturbation equations for the resulting smooth extended sources. This provides an end-to-end gravitational EES implementation for eccentric motion and validates a computational ingredient needed for extending frequency-domain effective-source calculations toward second order.
ER -