A conformal isothermal reformulation of optical geometry converts the Gauss-Bonnet area term for weak deflection into boundary integrals evaluated on a flat reference ray, reproducing known finite-distance results for Schwarzschild, Reissner-Nordström, and Kottler spacetimes.
Mixed citations
Applications of the Gauss-Bonnet theorem to gravitational lensing
Mixed citation behavior. Most common role is background (60%).
7
Pith papers citing it
Background
60% of classified citations
abstract
In this geometrical approach to gravitational lensing theory, we apply the Gauss-Bonnet theorem to the optical metric of a lens, modelled as a static, spherically symmetric, perfect non-relativistic fluid, in the weak deflection limit. We find that the focusing of the light rays emerges here as a topological effect, and we introduce a new method to calculate the deflection angle from the Gaussian curvature of the optical metric. As examples, the Schwarzschild lens, the Plummer sphere and the singular isothermal sphere are discussed within this framework.
citation-role summary
background 3
method 2
citation-polarity summary
fields
gr-qc 7years
2026 7verdicts
UNVERDICTED 7representative citing papers
Hadrons described by the nonlinear sigma model minimally coupled to Maxwell theory modify photon paths away from null geodesics, enabling analytic hadronic corrections to gravitational lensing deflection angles.
A thermodynamic-optical duality reparameterizes black hole mass via observable shadow radius to derive lensing angles, Hawking temperature, and luminosity for Kerr, Kerr-MOG, and rotating Horndeski metrics, yielding model-specific signatures under EHT constraints including up to 52% deviation in Hor
A reference-renormalized curvature-primitive Gauss-Bonnet formalism computes finite-distance weak deflection angles in static spherical spacetimes without invoking photon spheres.
Higher-curvature EFT terms modify the photon sphere radius, critical impact parameter, and strong deflection coefficients, providing sensitive probes for constraints on quantum gravity effects via lensing and QNM spectra.
Computations for a new black hole metric with magnetic charge and Hernquist halo show that charge raises QNM frequencies while the halo lowers them, with similar opposing effects on shadow size and neutrino annihilation efficiency.
Topological numbers categorize black hole systems into universality classes based on thermodynamic behavior, with calculations for critical points and phase transitions.
citing papers explorer
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Boundary-only weak deflection angles from isothermal optical geometry
A conformal isothermal reformulation of optical geometry converts the Gauss-Bonnet area term for weak deflection into boundary integrals evaluated on a flat reference ray, reproducing known finite-distance results for Schwarzschild, Reissner-Nordström, and Kottler spacetimes.
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Hadronic lensing
Hadrons described by the nonlinear sigma model minimally coupled to Maxwell theory modify photon paths away from null geodesics, enabling analytic hadronic corrections to gravitational lensing deflection angles.
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Shadow dependent phenomenology framework for rotating black hole metric
A thermodynamic-optical duality reparameterizes black hole mass via observable shadow radius to derive lensing angles, Hawking temperature, and luminosity for Kerr, Kerr-MOG, and rotating Horndeski metrics, yielding model-specific signatures under EHT constraints including up to 52% deviation in Hor
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Reference-renormalized curvature-primitive Gauss-Bonnet formalism for finite-distance weak gravitational lensing in static spherical spacetimes
A reference-renormalized curvature-primitive Gauss-Bonnet formalism computes finite-distance weak deflection angles in static spherical spacetimes without invoking photon spheres.
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Photon Surfaces in Higher-Curvature Gravity: Implications for Quasinormal Modes and Gravitational Lensing
Higher-curvature EFT terms modify the photon sphere radius, critical impact parameter, and strong deflection coefficients, providing sensitive probes for constraints on quantum gravity effects via lensing and QNM spectra.
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Quasinormal Modes and Neutrino Energy Deposition for a Magnetically Charged Black Hole in a Hernquist Dark Matter Halo
Computations for a new black hole metric with magnetic charge and Hernquist halo show that charge raises QNM frequencies while the halo lowers them, with similar opposing effects on shadow size and neutrino annihilation efficiency.
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Topology of black hole thermodynamics: A brief review
Topological numbers categorize black hole systems into universality classes based on thermodynamic behavior, with calculations for critical points and phase transitions.