2008/06/17 by Thomas P. Kling, Thomas Kling, Bryan Campbell
Physics and Astronomy · #Astrophysical Phenomena and Observations #Galaxies: Formation, Evolution, Phenomena #Pulsars and Gravitational Waves Research #astro-ph #gr-qc
paper · pdf · doi:10.1103/physrevd.77.123012
published as Phys.Rev.D77:123012,2008 · accepted to Phys. Rev. D
arxiv created 2008/06/17 · openalex publication_date 2008/06/24 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01
Using the Newman and Penrose [E. T. Newman and R. Penrose, J. Math. Phys. (N.Y.) 3, 566 (1962).] spin-coefficient formalism, we examine the full Bianchi identities of general relativity in the context of gravitational lensing, where the matter and space-time curvature are projected into a lens plane perpendicular to the line of sight. From one component of the Bianchi identity, we provide a rigorous, new derivation of a Poisson equation for the projected matter density where the source term involves second derivatives of the observed weak gravitational lensing shear. We also show that the other components of the Bianchi identity reveal no new results. Numerical integration of the Poisson equation in test cases shows an accurate mass map can be constructed from the combination of a ground-based, wide-field image and a Hubble Space Telescope image of the same system.