Frequency-domain self-force calculations using Gegenbauer reconstruction
arXiv:2509.19439 · doi:10.1103/9qsl-pr63
Abstract
We investigate the use of the Gegenbauer procedure for time-domain reconstruction in frequency-domain calculations of the self-force on a particle orbiting a black hole. The conventional technique relies on the so-called method of extended homogeneous solutions (EHSs), which circumvents the Gibbs phenomenon that would otherwise hamper the reconstruction of the particle's field from frequency modes. Unfortunately, the effectiveness of EHS reconstruction deteriorates rapidly with increasing orbital eccentricity, due to large numerical cancellations between frequency-mode contributions. Furthermore, the method is only suitable for bound orbits and cannot be fully applied in scattering scenarios. The Gegenbauer reconstruction procedure involves a reprojection of the partial Fourier representation onto a complementary basis of polynomials. The resulting series converges exponentially while averting the cancellation problem. We demonstrate the procedure with numerical results for the spherical harmonic modes of the scalar field sourced by a scalar charge in orbit around a Schwarzschild black hole. We illustrate the merits of this approach, and discuss the challenges that remain for a full Gegenbauer-based self-force calculation.
23 pages, 12 figures; v2 typographic changes to match published version
References in corpus (18)
- SciPy 1.0--Fundamental Algorithms for Scientific Computing in Python
- Self-force and radiation reaction in general relativity
- Classical and quantum scattering in post-Minkowskian gravity
- Gravitational self-force on generic bound geodesics in Kerr spacetime
- Gravitational self-force from radiation-gauge metric perturbations
- Gravitational self-force on eccentric equatorial orbits around a Kerr black hole
- Frequency-domain calculation of the self force: the high-frequency problem and its resolution
- Self-force effects in post-Minkowskian scattering
- Comparison of post-Minkowskian and self-force expansions: Scattering in a scalar charge toy model
- Waveform Modelling for the Laser Interferometer Space Antenna
- Gravitational perturbations of rotating black holes in Lorenz gauge
- Self-force correction to the deflection angle in black-hole scattering: a scalar charge toy model
- Gravitational Scattering and Beyond from Extreme Mass Ratio Effective Field Theory
- Time-domain metric reconstruction for hyperbolic scattering
- Metric perturbations of Kerr spacetime in Lorenz gauge: Circular equatorial orbits
- Black hole scattering near the transition to plunge: Self-force and resummation of post-Minkowskian theory
- Frequency-domain approach to self-force in hyperbolic scattering
- Sourced metric perturbations of Kerr spacetime in Lorenz gauge