Continuous Limit of Multiple Gravitational Lens Effect and Average Magnification Factor

Yoshida, Hiroshi; Nakamura, Kouji; Omote, Minoru

Continuous Limit of Multiple Gravitational Lens Effect and Average Magnification Factor

Authors

Yoshida, Hiroshi

Nakamura, Kouji

Omote, Minoru

Description

We show that the gravitational magnification factor averaged over all configurations of lenses in a locally inhomogeneous universe satisfy a second order differential equation with redshift $z$ by taking the continuous limit of multi-plane gravitational lens equation (the number $N$ of lenses $\to\infty$) and that the gravitationally magnified Dyer-Roeder distance in a clumpy universe becomes to that of the Friedmann-Lema\^ıtre universe for arbitrary values of the density parameter $Ω_{0}$ and of a mass fraction $\barα$ (smoothness parameter).
13 pages, 2 figures