我們透過分析電磁波的格林函數來研究電磁波在球形時空中的傳播。我們採用純量向量分 解來求解 2 球面上的麥克斯韋方程組，並僅根據純量格林函數表達其解。然後，我們概述了 一種使用 integral-differential operator 從熱核計算相關格林函數的方法，該算子將不同維度 的相應熱核關聯起來，以便所有這些都可以從 1維球體解生成。我們將此方法應用於 2 維 和 3 維球體，並獲得有質量和無質量格林函數的結果。我們注意到，當質量下降到由空間維 度D 確定的某個值以下時，我們的結果顯示出非因果傳播。突出的因果關係問題。 ;We here study the propagation of electromagnetic waves in spherical spacetimes by analyz- ing their Green’s functions. We employ a scalar-vector decomposition to solve Maxwell’s equations on the 2-sphere and write their solutions solely in terms of scalar Green’s func- tions. We then outline a method for calculating the relevant Green’s functions from their heat kernels using an integral-differential operator which relates the corresponding heat kernels in different dimensions, so that all of them may be generated from the 1-sphere solution. We apply this method to the 2 and 3 dimensional spheres and obtain results for both the the massive and massless Green’s functions. We note that our results display acausal propagation when the mass drops below a certain value determined by the spatial dimension D. In the future, we hope to extend our results to general dimensional spherical spacetimes and address any outstanding causality issues that remain.
