The Quadruple Image Configurations of Asymptotically Circular Gravitational Lenses. (arXiv:2205.06269v1 [gr-qc])
<a href="http://arxiv.org/find/gr-qc/1/au:+Falor_C/0/1/0/all/0/1">Chirag Falor</a>, <a href="http://arxiv.org/find/gr-qc/1/au:+Schechter_P/0/1/0/all/0/1">Paul L. Schechter</a>
The quadruple image configurations of gravitational lenses with vanishing
ellipticity are examined. Even though such lenses asymptotically approach
circularity, the configurations are stable if the position of the source
relative to the vanishing diamond caustic is held constant. The configurations
are the solutions of a quartic equation, an “Asymptotically Circular Lens
Equation” (ACLE), parameterized by a single complex quantity. Several
alternative parameterizations are examined. Relative magnifications of the
images are derived. When a non-vanishing quadrupole, in the form of an external
shear (XS), is added to the singular isothermal sphere (SIS), its
configurations emerge naturally as stretched and squeezed versions of the
circular configurations. And as the SIS+XS model is a good first approximation
for most quadruply lensed quasars, their configurations likewise have only 2+1
salient dimensions. The asymptotically circular configurations can easily be
adapted to the problem of Solar System “occultation flashes.”
The quadruple image configurations of gravitational lenses with vanishing
ellipticity are examined. Even though such lenses asymptotically approach
circularity, the configurations are stable if the position of the source
relative to the vanishing diamond caustic is held constant. The configurations
are the solutions of a quartic equation, an “Asymptotically Circular Lens
Equation” (ACLE), parameterized by a single complex quantity. Several
alternative parameterizations are examined. Relative magnifications of the
images are derived. When a non-vanishing quadrupole, in the form of an external
shear (XS), is added to the singular isothermal sphere (SIS), its
configurations emerge naturally as stretched and squeezed versions of the
circular configurations. And as the SIS+XS model is a good first approximation
for most quadruply lensed quasars, their configurations likewise have only 2+1
salient dimensions. The asymptotically circular configurations can easily be
adapted to the problem of Solar System “occultation flashes.”
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