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A Cusp—Counting Formula For Caustics Due To Multiplane Gravitational Lensing

Published online by Cambridge University Press:  25 May 2016

A. O. Petters
A. O. Petters*
Affiliation:
Princeton University, Department of Mathematics, Princeton, NJ 08544, USA

Extract

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Consider a gravitational lens system with K planes. If light rays are traced back from the observer to the light source plane, then the points on the first lens plane where a light ray either terminates, or, passes through and terminates before reaching the light source plane, are “obstruction points.” More precisely, tracing rays back to the source plane induces a K-plane lensing map η : U ⊆ R2 → R2 of the form η(x1) = x1 −∑i=1k αi(xi(xi)). We then define an obstruction point of η to be a point a of U where limx1→a |αi(xi(x1))| = ∞ for some “deflection angle” αi.

Type
Chapter 8: Quasar Structure & Microlensing
Information
Symposium - International Astronomical Union , Volume 173: Astrophysical Applications of Gravitational Lensing , 1996 , pp. 281 - 282
Copyright
Copyright © Kluwer 1996 

References

Petters, A.O., 1995, J Math Phys, in press.Google Scholar
Levine, H., Petters, A.O., & Wambsganss, J., 1993, J Math Phys, 34(10), 4781 Google Scholar