Math @ Duke

Publications [#243989] of Arlie O. Petters
Papers Published
 Petters, AO; Witt, H, Bounds on Number of Cusps Due to Point Mass Gravitional Lenses with Continuous Matter and Shear,
J. Math. Phys., vol. 37 no. 2920
(1996),
pp. 29202933 [doi]
(last updated on 2019/06/19)
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 σc is 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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