Reference-renormalized curvature-primitive Gauss-Bonnet formalism for finite-distance weak gravitational lensing in static spherical spacetimes
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arXiv
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| Format: | Preprint |
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2026
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| author | Pantig, Reggie C. Övgün, Ali |
| author_facet | Pantig, Reggie C. Övgün, Ali |
| contents | We develop a reference-renormalized (photon-sphere-free) normalization scheme for Gauss-Bonnet gravitational lensing at finite distance in static, spherically symmetric spacetimes. The method treats the curvature primitive used to reduce the Gauss-Bonnet curvature-area integral as a quantity defined only modulo an additive constant (an additive gauge freedom). We fix this gauge by matching to a physically chosen reference optical geometry in an outer regime where the physical geometry approaches that reference, thereby defining a unique renormalized discrepancy primitive $\mathcal{P}_e(r)$ by reference subtraction. The resulting master formula yields the Ishihara-Li finite-distance deflection angle without invoking any circular null orbit, while remaining fully compatible with orbit-normalized prescriptions whenever a suitable photon sphere exists (the two gauges differ only by a constant shift and give identical $α$). In asymptotically flat settings the canonical reference is Minkowski, while in Kottler-type backgrounds the canonical reference is de Sitter within the static patch, making the operational fiducial explicit. We validate the method by reproducing Ishihara's finite-distance weak-deflection formulas for Schwarzschild, Reissner-Nordström, and Kottler spacetimes, including the mixed $r_gΛ$ term in the Kottler case within the static-patch fiducial. We also present a demonstrative example in which orbit normalization is genuinely inapplicable because no circular null orbit exists in the physical optical region (the Janis-Newman-Winicour spacetime for $γ\le \tfrac12$). The result is a unified, geometrically transparent route to finite-distance lensing that preserves compatibility with orbit-normalized prescriptions whenever those apply. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_16807 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Reference-renormalized curvature-primitive Gauss-Bonnet formalism for finite-distance weak gravitational lensing in static spherical spacetimes Pantig, Reggie C. Övgün, Ali General Relativity and Quantum Cosmology High Energy Physics - Theory We develop a reference-renormalized (photon-sphere-free) normalization scheme for Gauss-Bonnet gravitational lensing at finite distance in static, spherically symmetric spacetimes. The method treats the curvature primitive used to reduce the Gauss-Bonnet curvature-area integral as a quantity defined only modulo an additive constant (an additive gauge freedom). We fix this gauge by matching to a physically chosen reference optical geometry in an outer regime where the physical geometry approaches that reference, thereby defining a unique renormalized discrepancy primitive $\mathcal{P}_e(r)$ by reference subtraction. The resulting master formula yields the Ishihara-Li finite-distance deflection angle without invoking any circular null orbit, while remaining fully compatible with orbit-normalized prescriptions whenever a suitable photon sphere exists (the two gauges differ only by a constant shift and give identical $α$). In asymptotically flat settings the canonical reference is Minkowski, while in Kottler-type backgrounds the canonical reference is de Sitter within the static patch, making the operational fiducial explicit. We validate the method by reproducing Ishihara's finite-distance weak-deflection formulas for Schwarzschild, Reissner-Nordström, and Kottler spacetimes, including the mixed $r_gΛ$ term in the Kottler case within the static-patch fiducial. We also present a demonstrative example in which orbit normalization is genuinely inapplicable because no circular null orbit exists in the physical optical region (the Janis-Newman-Winicour spacetime for $γ\le \tfrac12$). The result is a unified, geometrically transparent route to finite-distance lensing that preserves compatibility with orbit-normalized prescriptions whenever those apply. |
| title | Reference-renormalized curvature-primitive Gauss-Bonnet formalism for finite-distance weak gravitational lensing in static spherical spacetimes |
| topic | General Relativity and Quantum Cosmology High Energy Physics - Theory |
| url | https://arxiv.org/abs/2604.16807 |