Advances in Astronomy and Space Physics, Volume 2, Issue 2 (2012)

Gravitational lens equation: critical solutions and magnification near folds and cusps

A. N. Alexandrov1, S. M. Koval2, V. I. Zhdanov1

1Astronomical Observatory, Taras Shevchenko National University of Kyiv, Observatorna str., 4, 04053, Kyiv, Ukraine
2National University of Kyiv-Mohyla Academy, Skovorody str., 2, 04655, Kyiv, Ukraine

Abstract
We study approximate solutions of the gravitational lens equation and corresponding lens magnification factor near the critical point. This consideration is based on the Taylor expansion of the lens potential in powers of coordinates and an introduction of a proximity parameter characterising the closeness of a point source to the caustic. Second-order corrections to known approximate solutions and magnification are found in case of a general fold point. The first-order corrections near a general cusp are found as well.

Keywords:
gravitational lensing, methods: analytical