Retarded Green Function For Bopp--Podolsky Electrodynamics in Four-Dimensional De Sitter Spacetime
Abstract
We study classical Bopp--Podolsky (BP) electrodynamics on four-dimensional de Sitter spacetime, focusing on its transverse retarded Green function and gauge-invariant electromagnetic response. Because de Sitter spacetime is maximally symmetric, its vector Green functions admit a covariant expansion in a finite basis of invariant bitensors, with scalar coefficients depending only on the invariant separation. For conserved sources, the fourth-order field operator factorizes into Maxwell and massive-vector operators, yielding the BP retarded kernel as the difference of their transverse Green functions. Using the invariant bitensor decomposition, we reduce the propagator equations to a hypergeometric master equation and determine the distributional structure of its solution. The common leading short-distance singularity of the Maxwell and massive-vector sectors cancels, leaving a logarithmic master singularity and a softened vector-potential wavefront. After one curl, the gauge-invariant field-strength kernel contains a null-cone delta distribution and a regular timelike tail. The smooth Maxwell master tail is annihilated by the curl, so the interior electromagnetic tail is generated entirely by the massive sector. We also derive an exact horizon-regular static potential, demonstrate the cancellation of the Coulomb divergence, recover the flat-space BP potential, and formulate the generalized Gauss law. On global de Sitter spacetime, the compactness of the spatial sections requires the total charge to vanish; we implement this constraint using an antipodal charge configuration with smooth factorized initial data. The analysis is classical and does not assume a quantum Lee--Wick contour or a preferred de Sitter vacuum.
Related
- Spiral galaxy spacetime in extended scalar-tensor-Gauss-Bonnet gravity coupled to nonlinear electrodynamics
- Higher-Dimensional Slowly Rotating Black Holes in Nonlinear Electrodynamics
- Scattering of massless scalar waves by higher-dimensional regular black holes in general relativity coupled to nonlinear electrodynamics
- Static electric and magnetic traversable wormholes in (2+1)-dimensional nonlinear electrodynamics
- Black objects in a five-dimensional swirling spacetime
BibTeX
@misc{fan2026retarded,
title = {{Retarded Green Function For Bopp--Podolsky Electrodynamics in Four-Dimensional De Sitter Spacetime}},
author = {Wei Fan and Xiao Yan Chew},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.16239},
eprint = {2610.16239},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.16239},
note = {CC BY-NC-SA 4.0},
}
RIS
TY - UNPB
TI - Retarded Green Function For Bopp--Podolsky Electrodynamics in Four-Dimensional De Sitter Spacetime
AU - Wei Fan
AU - Xiao Yan Chew
PY - 2026
DA - 2026/10/12
PB - arXiv
DO - 10.48550/arxiv.2610.16239
UR - https://arxiv.org/abs/2610.16239
AB - We study classical Bopp--Podolsky (BP) electrodynamics on four-dimensional de Sitter spacetime, focusing on its transverse retarded Green function and gauge-invariant electromagnetic response. Because de Sitter spacetime is maximally symmetric, its vector Green functions admit a covariant expansion in a finite basis of invariant bitensors, with scalar coefficients depending only on the invariant separation. For conserved sources, the fourth-order field operator factorizes into Maxwell and massive-vector operators, yielding the BP retarded kernel as the difference of their transverse Green functions. Using the invariant bitensor decomposition, we reduce the propagator equations to a hypergeometric master equation and determine the distributional structure of its solution. The common leading short-distance singularity of the Maxwell and massive-vector sectors cancels, leaving a logarithmic master singularity and a softened vector-potential wavefront. After one curl, the gauge-invariant field-strength kernel contains a null-cone delta distribution and a regular timelike tail. The smooth Maxwell master tail is annihilated by the curl, so the interior electromagnetic tail is generated entirely by the massive sector. We also derive an exact horizon-regular static potential, demonstrate the cancellation of the Coulomb divergence, recover the flat-space BP potential, and formulate the generalized Gauss law. On global de Sitter spacetime, the compactness of the spatial sections requires the total charge to vanish; we implement this constraint using an antipodal charge configuration with smooth factorized initial data. The analysis is classical and does not assume a quantum Lee--Wick contour or a preferred de Sitter vacuum.
ER -