发表机构
Ningbo University; Huazhong University of Science and Technology（宁波大学; 华中科技大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该研究针对史瓦西时空中的偏心轨道，构建实现了一阶 Lorenz 规范 GSF 的频域 EES 公式化方法，通过解析延拓分支克服收敛问题，提供了偏心运动的端到端引力 EES 实现并验证了二阶扩展所需计算要素。
AI 中文摘要
有效源公式化方法为无法直接逐模处理奇异 retarded 场时的引力自作用力（GSF）计算提供了实用途径。迄今为止，仅通过有效源方法得到了史瓦西时空中圆轨道的一阶频域 GSF。我们构建并实现了适用于史瓦西时空中偏心轨道的一阶 Lorenz 规范 GSF 的频域扩展有效源（EES）公式化方法。核心障碍在于径向 libration 会迫使物理 puncture 和有效源在内部与外部分支之间切换，限制了它们的可微性并导致谱收敛缓慢。我们通过在 libration 区域上解析延拓两个分支，并求解所得平滑扩展源的耦合 Lorenz 规范微扰方程，克服了这一障碍。这为偏心运动提供了端到端的引力 EES 实现，并验证了将频域有效源计算扩展至二阶所需的计算要素。
英文摘要
Effective-source formulations provide a practical route to gravitational self-force (GSF) calculations when singular retarded fields cannot be handled directly mode by mode. Up to now, only frequency-domain first-order GSF for circular orbits in Schwarzschild spacetime was obtained with the effective-source method. We construct and implement a frequency-domain extended effective-source (EES) formulation for first-order Lorenz-gauge GSF on eccentric orbits in Schwarzschild spacetime. The central obstacle is that radial libration forces the physical puncture and effective source to switch between interior and exterior branches, limiting their differentiability and producing slow spectral convergence. We overcome this obstruction by analytically extending both branches across the libration region and solving the coupled Lorenz-gauge perturbation equations for the resulting smooth extended sources. This provides an end-to-end gravitational EES implementation for eccentric motion and validates a computational ingredient needed for extending frequency-domain effective-source calculations toward second order.
Comments31 pages, 3 figures
