Poisson equation for weak gravitational lensing

Journal Article · Sun Jun 15 00:00:00 EDT 2008 · Physical Review. D, Particles Fields

DOI:https://doi.org/10.1103/PHYSREVD.77.123012· OSTI ID:21212004

Kling, Thomas P; Campbell, Bryan ^[1]

---

1. Department of Physics, Bridgewater State College, Bridgewater, Massachusetts 02325 (United States)

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.

• OSTI ID: 21212004
• Journal Information: Physical Review. D, Particles Fields, Vol. 77, Issue 12; Other Information: DOI: 10.1103/PhysRevD.77.123012; (c) 2008 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA); ISSN 0556-2821
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
DENSITY
GENERAL RELATIVITY THEORY
GRAVITATIONAL WAVES
MASS
POISSON EQUATION
SPACE-TIME
SPIN
TELESCOPES