Characteristic evolution of conformal scattering: I. Scalar Waves in Minkowski Spacetime
Abstract
We study the conformal scattering of massless scalar waves in Minkowski spacetime. The conformal scattering problem is formulated as a Goursat (characteristic initial-value) problem of the physical wave equation in compactified double-null coordinates, including the neighborhood of spatial infinity i0. As null infinities ℐ± lie on the domain boundary by construction, asymptotic radiation is directly accessible. We consider three physical scenarios: free wave propagation, scattering off a Pöschl--Teller (PT) potential, and the semi-linear |ϕ|n−1ϕ wave equation. For multipole numbers ℓ =0,1, an explicit stencil, averaging along the spatial direction, yields globally second-order convergent results. For ℓ ≥ 2, an implicit stencil averaging along the temporal direction is required for numerical stability. Although the singular i0 reduces the convergence of the radiation data on ℐ+ to first order, Richardson extrapolation enhances the effective convergence rate to approximately $1.5$. For PT scattering, our method accurately computes scattering quantities, notably the phase shifts induced by the potential. In the semi-linear case, our method captures the physical signatures of a self-defocusing Kerr nonlinearity, including self-phase modulation and spectral broadening. The compactified double-null framework proves to be simple and efficient, suggesting a promising approach to the global evolution of conformal scattering.
Versions
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BibTeX
@misc{he2026characteristic,
title = {{Characteristic evolution of conformal scattering: I. Scalar Waves in Minkowski Spacetime}},
author = {Zhen-Tao He and Yu Tian and Hongbao Zhang},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2608.15729},
eprint = {2608.15729},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2608.15729},
}
RIS
TY - UNPB
TI - Characteristic evolution of conformal scattering: I. Scalar Waves in Minkowski Spacetime
AU - Zhen-Tao He
AU - Yu Tian
AU - Hongbao Zhang
PY - 2026
DA - 2026/10/07
PB - arXiv
DO - 10.48550/arxiv.2608.15729
UR - https://arxiv.org/abs/2608.15729
AB - We study the conformal scattering of massless scalar waves in Minkowski spacetime. The conformal scattering problem is formulated as a Goursat (characteristic initial-value) problem of the physical wave equation in compactified double-null coordinates, including the neighborhood of spatial infinity i^0. As null infinities ℐ^± lie on the domain boundary by construction, asymptotic radiation is directly accessible. We consider three physical scenarios: free wave propagation, scattering off a Pöschl--Teller (PT) potential, and the semi-linear |ϕ|^n−1ϕ wave equation. For multipole numbers ℓ =0,1, an explicit stencil, averaging along the spatial direction, yields globally second-order convergent results. For ℓ ≥ 2, an implicit stencil averaging along the temporal direction is required for numerical stability. Although the singular i^0 reduces the convergence of the radiation data on ℐ^+ to first order, Richardson extrapolation enhances the effective convergence rate to approximately $1.5$. For PT scattering, our method accurately computes scattering quantities, notably the phase shifts induced by the potential. In the semi-linear case, our method captures the physical signatures of a self-defocusing Kerr nonlinearity, including self-phase modulation and spectral broadening. The compactified double-null framework proves to be simple and efficient, suggesting a promising approach to the global evolution of conformal scattering.
ER -