Poisson equation for weak gravitational lensing

Details Poisson equation for weak gravitational lensing Poisson equation for weak gravitational lensing

2008-06-17

arxiv.org/abs/0806.2834v1

Phys.Rev.D77:123012,2008

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

accepted to Phys. Rev. D

Scientific paper

10.1103/PhysRevD.77.123012

Using the Newman and Penrose spin coefficient (NP) 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.

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