Pseudo-spectral methods in gravitational lensing: Spin precession in loop quantum black hole spacetimes
Abstract
Gravitational lensing is usually treated as an initial value problem: for a given impact parameter of an unbound orbit, one computes the resulting deflection angle. In this paper we advocate the inverse point of view. For a prescribed deflection angle, the orbit is selected by two boundary conditions at spatial infinity, so that the lensing problem becomes a well-defined two-point boundary value problem, with the impact parameter playing the role of a nonlinear eigenvalue. We show that pseudo-spectral methods based on Chebyshev collocation solve this boundary value problem accurately at modest computational cost, and that the parallel transport equations governing the spin precession of the particle reduce to a single linear system on the same grid. As a concrete application, we compute the spin precession of massive particles in backward scattering off two black hole spacetimes from loop quantum gravity, the covariant effective metric and the self-dual loop quantum black hole. We find that the quantum corrections are most pronounced for slowly moving particles, while in the ultra-relativistic limit the universal spin flip is always recovered. The flip itself is universal, but the rate at which it is approached is not. The derivative of cosξ with respect to the particle speed at v=1 depends on the quantum parameters of both spacetimes. The framework is not restricted to the models studied here and applies to any static, spherically symmetric spacetime.
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BibTeX
@misc{pang2026pseudospectral,
title = {{Pseudo-spectral methods in gravitational lensing: Spin precession in loop quantum black hole spacetimes}},
author = {Xiankai Pang and Xiao-Kan Guo},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.18064},
eprint = {2610.18064},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.18064},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Pseudo-spectral methods in gravitational lensing: Spin precession in loop quantum black hole spacetimes
AU - Xiankai Pang
AU - Xiao-Kan Guo
PY - 2026
DA - 2026/10/22
PB - arXiv
DO - 10.48550/arxiv.2610.18064
UR - https://arxiv.org/abs/2610.18064
AB - Gravitational lensing is usually treated as an initial value problem: for a given impact parameter of an unbound orbit, one computes the resulting deflection angle. In this paper we advocate the inverse point of view. For a prescribed deflection angle, the orbit is selected by two boundary conditions at spatial infinity, so that the lensing problem becomes a well-defined two-point boundary value problem, with the impact parameter playing the role of a nonlinear eigenvalue. We show that pseudo-spectral methods based on Chebyshev collocation solve this boundary value problem accurately at modest computational cost, and that the parallel transport equations governing the spin precession of the particle reduce to a single linear system on the same grid. As a concrete application, we compute the spin precession of massive particles in backward scattering off two black hole spacetimes from loop quantum gravity, the covariant effective metric and the self-dual loop quantum black hole. We find that the quantum corrections are most pronounced for slowly moving particles, while in the ultra-relativistic limit the universal spin flip is always recovered. The flip itself is universal, but the rate at which it is approached is not. The derivative of cosξ with respect to the particle speed at v=1 depends on the quantum parameters of both spacetimes. The framework is not restricted to the models studied here and applies to any static, spherically symmetric spacetime.
ER -