Continuous Limit of Multiple Lens Effect and the Optical Scalar Equation

Details Continuous Limit of Multiple Lens Effect and the Optical Scalar Equation Continuous Limit of Multiple Lens Effect and the Optical Scalar Equation

2004-07-02

arxiv.org/abs/astro-ph/0407040v1

Mon.Not.Roy.Astron.Soc. 358 (2005) 39-48

Astronomy and Astrophysics

Astrophysics

20 pages

Scientific paper

10.1111/j.1365-2966.2005.08698.x

We study the continuous limit of the multiple gravitational lensing theory based on the thin lens approximation. Under the approximation, we define a new, light-path dependent angular diameter distance $\tilde{d}$ and show that it satisfies the optical scalar equation. The distance provides relations between quantities used in the gravitational lensing theory (the convergence-, the shear- and the twist-term) and those used in the scalar optics theory (the rates of expansion, shear and rotation).

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