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Bibliographic Details
Main Author: Gorenstein, Marc V.
Format: Preprint
Published: 2026
Subjects:
Online Access:https://arxiv.org/abs/2601.01614
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Table of Contents:
  • In gravitational lensing, the Mass-Sheet Transformation (MST)-or mass-sheet degeneracy-leaves image positions unchanged while scaling magnifications and time delays. The transformation scales the lens mass distribution and superposes a uniform mass sheet, but this formulation offers no clear physical interpretation. Here I show that the MST follows directly from a scaling symmetry that becomes apparent when the ray-trace relation is written in proper-distance coordinates. In this form, the ray-trace relation isolates a geometric focusing term. Subtracting this term from the deflection law defines the Image-Selection Relation (ISR), which determines image positions, magnifications, and differential time delays. The ISR exhibits a scaling symmetry that leaves image positions unchanged while scaling magnifications and time delays. Restoring the geometric focusing term then gives a ray-trace relation related to the original one by the Mass-Sheet Transformation.