Gravitational lensing time delay beyond the Shapiro/geometry split
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866911693988167680 |
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| author | Teodori, Luca Blum, Kfir Bai, Zhaoyu |
| author_facet | Teodori, Luca Blum, Kfir Bai, Zhaoyu |
| contents | Time delays are a key observable in strong gravitational lensing systems. Their theoretical expression is usually written as a sum of a geometrical delay and a Shapiro delay, with cosmology entering through angular diameter distances and a redshift prefactor. In this work we derive this structure from the exact null geodesics of the Schwarzschild-de Sitter metric. The standard formula is recovered as the leading term in a small-angle expansion, and we identify the first correction to the usual geometrical-plus-Shapiro split. Such correction does not introduce any new cosmological dependence: it corresponds instead to a higher-order correction intrinsic to the Schwarzschild part of the metric. As a consequence, up to this order, the cosmological constant enters only through the unlensed angular diameter distances and the unlensed lens-redshift prefactor. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2605_18182 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Gravitational lensing time delay beyond the Shapiro/geometry split Teodori, Luca Blum, Kfir Bai, Zhaoyu Cosmology and Nongalactic Astrophysics General Relativity and Quantum Cosmology Time delays are a key observable in strong gravitational lensing systems. Their theoretical expression is usually written as a sum of a geometrical delay and a Shapiro delay, with cosmology entering through angular diameter distances and a redshift prefactor. In this work we derive this structure from the exact null geodesics of the Schwarzschild-de Sitter metric. The standard formula is recovered as the leading term in a small-angle expansion, and we identify the first correction to the usual geometrical-plus-Shapiro split. Such correction does not introduce any new cosmological dependence: it corresponds instead to a higher-order correction intrinsic to the Schwarzschild part of the metric. As a consequence, up to this order, the cosmological constant enters only through the unlensed angular diameter distances and the unlensed lens-redshift prefactor. |
| title | Gravitational lensing time delay beyond the Shapiro/geometry split |
| topic | Cosmology and Nongalactic Astrophysics General Relativity and Quantum Cosmology |
| url | https://arxiv.org/abs/2605.18182 |