Gravitational lens equation for embedded lenses; magnification and ellipticity
Abstract
We give the lens equation for light deflections caused by point mass condensations in an otherwise spatially homogeneous and flat universe. We assume the signal from a distant source is deflected by a single condensation before it reaches the observer. We call this deflector an embedded lens because the deflecting mass is part of the mean density. The embedded lens equation differs from the conventional lens equation because the deflector mass is not simply an addition to the cosmic mean. We prescribe an iteration scheme to solve this new lens equation and use it to compare our results with standard linear lensing theory. We also compute analytic expressions for the lowest order corrections to image amplifications and distortions caused by incorporating the lensing mass into the mean. We use these results to estimate the effect of embedding on strong lensing magnifications and ellipticities and find only small effects, <1%, contrary to what we have found for time delays and for weak lensing, ∼5%.
- Publication:
-
Physical Review D
- Pub Date:
- October 2011
- DOI:
- 10.1103/PhysRevD.84.083004
- arXiv:
- arXiv:1106.2205
- Bibcode:
- 2011PhRvD..84h3004C
- Keywords:
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- 98.62.Sb;
- Gravitational lenses and luminous arcs;
- Astrophysics - Cosmology and Nongalactic Astrophysics;
- General Relativity and Quantum Cosmology
- E-Print:
- 4 figures