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Recursion relations for gravitational lensing
General Relativity and Gravitation ( IF 2.8 ) Pub Date : 2020-03-01 , DOI: 10.1007/s10714-020-02677-z
Ben David Normann , Chris Clarkson

The weak gravitational lensing formalism can be extended to the strong lensing regime by integrating a nonlinear version of the geodesic deviation equation. The resulting ‘roulette’ expansion generalises the notion of convergence, shear and flexion to arbitrary order. The independent coefficients of this expansion are screen space gradients of the optical tidal tensor which approximates to the usual lensing potential in the weak field limit. From lensed images, knowledge of the roulette coefficients can in principle be inverted to reconstruct the mass distribution of a lens. In this paper, we simplify the roulette expansion and derive a family of recursion relations between the various coefficients, generalising the Kaiser–Squires relations beyond the weak-lensing regime.

中文翻译:

引力透镜的递归关系

通过对测地线偏差方程的非线性版本进行积分,可以将弱引力透镜形式主义扩展到强透镜体系。由此产生的“轮盘赌”扩展将收敛、剪切和弯曲的概念概括为任意顺序。这种膨胀的独立系数是光学潮汐张量的屏幕空间梯度,它近似于弱场极限中的通常透镜势。从透镜图像,轮盘赌系数的知识原则上可以反转以重建透镜的质量分布。在本文中,我们简化了轮盘赌扩展并推导出了各种系数之间的一系列递归关系,将 Kaiser-Squires 关系推广到弱透镜机制之外。
更新日期:2020-03-01
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