Mathematics of gravitational lensing: multiple imaging and magnification

Petters, Arlie O.; Werner, Marcus C.

doi:10.1007/s10714-010-0968-6

Cited by 32 publications

(34 citation statements)

References 82 publications

(153 reference statements)

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“…Recall that an image is called a minimal, saddle or maximal image if it is a (local) minimum, saddle point or (local) maximum of the time delay function (induced from the lens potential corresponding to η); see e.g. [10,11]. The characterization via |R ′ | then follows from the equality of the Jacobian determinant of the lensing map and the determinant of the Hessian of the time delay function.…”

Section: Adding Tiny Masses To a Lensmentioning

confidence: 99%

Creating images by adding masses to gravitational point lenses

2015

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A well-studied maximal gravitational point lens construction of S. H. Rhie produces 5n images of a light source using n + 1 deflector masses. The construction arises from a circular, symmetric deflector configuration on n masses (producing only 3n + 1 images) by adding a tiny mass in the center of the other mass positions (and reducing all the other masses a little bit).In a recent paper we studied this "image creating effect" from a purely mathematical point of view (Sète, Luce & Liesen, Comput. Methods Funct. Theory 15(1):9-35, 2015). Here we discuss a few consequences of our findings for gravitational microlensing models. We present a complete characterization of the effect of adding small masses to these point lens models, with respect to the number of images. In particular, we give several examples of maximal lensing models that are different from Rhie's construction and that do not share its highly symmetric appearance. We give generally applicable conditions that allow the construction of maximal point lenses on n + 1 masses from maximal lenses on n masses.

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Section: Adding Tiny Masses To a Lensmentioning

confidence: 99%

Creating images by adding masses to gravitational point lenses

2015

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“…The analysis of such rational harmonic functions has received considerable attention in recent years. As nicely explained in the expository article of Khavinson and Neumann [12], they have important applications in gravitational microlensing; see also the survey [18]. In addition they are related to the matrix theory problem of expressing certain adjoints of a diagonalizable matrix as a rational function in the matrix [15].…”

Section: Introductionmentioning

confidence: 99%

Perturbing Rational Harmonic Functions by Poles

Sète¹,

Luce²,

Liesen³

2014

Comput. Methods Funct. Theory

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We study how adding certain poles to rational harmonic functions of the form R(z) − z, with R(z) rational and of degree d ≥ 2, affects the number of zeros of the resulting functions. Our results are motivated by and generalize a construction of Rhie derived in the context of gravitational microlensing (arXiv:astro-ph/0305166). Of particular interest is the construction and the behavior of rational functions R(z) that are extremal in the sense that R(z)−z has the maximal possible number of 5(d −1) zeros.

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“…This type of equation is studied for astorophisists. For more explanation from astrophiscal viewpoint, see for example Petters-Werner [13]. The lens equation can be witten as…”

Section: Lens Equationmentioning

confidence: 99%

“…The equation of the real solutions of (6 ) reduces to z 2m−n (z n − a n ) = 1. (13) It is easy to see that there are two real solutions (one positive and one negative). See Figure 4.…”

Section: Observation 16mentioning

confidence: 99%

On the Roots of an Extended Lens Equation and an Application

Oka

2018

Springer Proceedings in Mathematics &Amp; Statistics

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We consider zero points of a generalized Lens equation L(z,z) =z m −p(z)/q(z) and also harmonically splitting Lens type equation L hs (z,z) = r(z) − p(z)/q(z) with deg q(z) = n, deg p(z) < n whose numerator is a mixed polynomials, say f (z,z), of degree (n + m; n, m). To such a polynomial, we associate a strongly mixed weighted homogeneous polynomial F (z,z) of two variables and we show the topology of Milnor fibration of F is described by the number of roots of f (z,z) = 0.2000 Mathematics Subject Classification. 14P05,14N99.

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Mathematics of gravitational lensing: multiple imaging and magnification

Cited by 32 publications

References 82 publications

Creating images by adding masses to gravitational point lenses

Creating images by adding masses to gravitational point lenses

Perturbing Rational Harmonic Functions by Poles

On the Roots of an Extended Lens Equation and an Application

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