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| Format: | Preprint |
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2026
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| Online Access: | https://arxiv.org/abs/2601.01614 |
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| _version_ | 1866912801757331456 |
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| author | Gorenstein, Marc V. |
| author_facet | Gorenstein, Marc V. |
| 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_01614 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | The Optical Origin of the Mass-Sheet Transformation Gorenstein, Marc V. Cosmology and Nongalactic Astrophysics 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. |
| title | The Optical Origin of the Mass-Sheet Transformation |
| topic | Cosmology and Nongalactic Astrophysics |
| url | https://arxiv.org/abs/2601.01614 |