Math @ Duke

Publications [#305706] of Arlie O. Petters
Papers Published
 Petters, AO; Witt, HJ, Bounds on number of cusps due to point mass gravitational lenses,
Journal of Mathematical Physics, vol. 37 no. 6
(June, 1996),
pp. 29202933, AIP Publishing [doi]
(last updated on 2019/02/15)
Abstract: Generic caustics in gravitational lensing occur locally either as folds or cusps. This paper rigorously proves that the total number of cusps, Ncusps, due to g point masses on a single plane having nonnormalized external shear γ>0 and continuous matter with constant density σc, is bounded as follows: 0≤Ncusps≤12g2. For vanishing shear γ=0 we obtain the result 0≤Ncusps≤12g(g1). Consequences of these bounds for the global geometry of caustics are discussed. It is also shown that if γ≥0 and σcis sufficiently large, then all cusps can be eliminated, that is, Ncusps=0. The paper also includes equations for calculating all the bicaustics (i.e., curves yielding the positions of cusps during a oneparameter evolution) of a single pointmass lens with continuous matter and shear. The methods of the paper are based on a new approach to pointmass gravitational lensing using complex quantities and the theory of resultants. © 1996 American Institute of Physics.


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