Abstract
Based on the standard gravitational lensing formalism with its effective, projected lensing potential in a given background cosmology, we investigated under which transformations of the source position and of the deflection angle the observable properties of the multiple images remain invariant. These observable properties are time delay differences, the relative image positions, relative shapes, and magnification ratios. As they only constrain local lens properties, we derive general, local invariance transformations in the areas covered by the multiple images. We show that the known global invariance transformations, for example, the mass-sheet transformation or the source position transformation, are contained in our invariance transformations, when they are restricted to the areas covered by the multiple images and when lens-model-based degeneracies are ignored, like the freedom to add or subtract masses in unconstrained regions without multiple images. Hence, we have identified the general class of invariance transformations that can occur, in particular in our model-independent local characterisation of strong gravitational lenses.
Highlights
Since the discovery by Falco et al (1985) that adding a constant mass sheet to the mass density of a gravitational lens model leaves the observable relative image positions and magnification ratios invariant, a lot of other invariance transformations have been found and investigated, for an overview see, for example, Gorenstein et al (1988), Liesenborgs & De Rijcke (2012), and Schneider & Sluse (2014) and references therein
We show that the known global invariance transformations, for example, the mass-sheet transformation or the source position transformation, are contained in our invariance transformations, when they are restricted to the areas covered by the multiple images and when lens-model-based degeneracies are ignored, like the freedom to add or subtract masses in unconstrained regions without multiple images
As no global connecting lens model is assumed in this approach, no additional monopoles are involved in the local version of the mass sheet transformation
Summary
Since the discovery by Falco et al (1985) that adding a constant mass sheet to the mass density of a gravitational lens model leaves the observable relative image positions and magnification ratios invariant, a lot of other invariance transformations have been found and investigated, for an overview see, for example, Gorenstein et al (1988), Liesenborgs & De Rijcke (2012), and Schneider & Sluse (2014) and references therein. 3, we investigate its general class of formalism-intrinsic invariance transformations in the absence of a lens model These transformations are locally confined to the areas covered by the multiple images, and are the invariance transformations that affect our model-independent lens characterisation. We show, how the model-independent parts can be derived from the general formalism-intrinsic invariance transformations developed in Sect. A different kind of invariance transformation, not considered here, was investigated in Schneider & Sluse (2013) and Wagner (2018), namely the degeneracy that arises if a lens model is split into two parts, for example, a main (axisymmetric) lens and a perturber.
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