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%).
10
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 10years
2026 10representative citing papers
CosmicDancePro integrates multimodal datasets to reveal that solar storms cause significant Starlink orbital decay and network degradation, and explains a 'W'-shaped altitude variation pattern via day-night atmospheric density differences.
A reference-renormalized curvature-primitive Gauss-Bonnet formalism computes finite-distance weak deflection angles in static spherical spacetimes without invoking photon spheres.
Derives spin-dependent bounds on NED deformation g/M from Sgr A* shadow, eikonal QNMs, and Comisso-Asenjo reconnection power in rotating geometries.
In a pion condensate, photons behave as massive particles and gravitational lensing gains a hadronic correction; the paper derives the modified ray equations and the deflection formula for a pionic-vortex black hole.
For a cubic-plus-quartic curvature EFT, photon-sphere and strong-lensing observables shift at first order in the couplings, but the impact-parameter formula is dimensionally wrong and the gravitational-wave QNM prediction is unproven.
Higher-curvature corrections induce polarization-dependent effective metrics for photons that shift photon spheres, alter eikonal quasinormal modes, and modify deflection angles in static spherically symmetric backgrounds.
Derives EFT corrections to deflection angle, photon sphere radius, critical impact parameter, and strong lensing coefficients for Reissner-Nordström black holes in weak and strong deflection regimes.
A diffeomorphic inversion re-parameterizes Kerr, Kerr-MOG, and Horndeski black hole observables in terms of the shadow radius, yielding model-specific deflection and luminosity scalings that break mass degeneracy.
Topological numbers categorize black hole systems into universality classes based on thermodynamic behavior, with calculations for critical points and phase transitions.
citing papers explorer
-
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.
-
Breaking Parameter Degeneracies in a Magnetically Charged Black Hole Embedded in a Hernquist Dark-Matter Halo: A Multi-Observable Analysis
CosmicDancePro integrates multimodal datasets to reveal that solar storms cause significant Starlink orbital decay and network degradation, and explains a 'W'-shaped altitude variation pattern via day-night atmospheric density differences.
-
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.
-
Energy extraction from NED-deformed rotating black holes via the Comisso-Asenjo reconnection process
Derives spin-dependent bounds on NED deformation g/M from Sgr A* shadow, eikonal QNMs, and Comisso-Asenjo reconnection power in rotating geometries.
-
Hadronic lensing
In a pion condensate, photons behave as massive particles and gravitational lensing gains a hadronic correction; the paper derives the modified ray equations and the deflection formula for a pionic-vortex black hole.
-
Photon Surfaces in Higher-Curvature Gravity: Implications for Quasinormal Modes and Gravitational Lensing
For a cubic-plus-quartic curvature EFT, photon-sphere and strong-lensing observables shift at first order in the couplings, but the impact-parameter formula is dimensionally wrong and the gravitational-wave QNM prediction is unproven.
-
Polarization-Dependent Photon Propagation, Quasinormal Modes, and Gravitational Lensing in Higher-Curvature Effective Theories
Higher-curvature corrections induce polarization-dependent effective metrics for photons that shift photon spheres, alter eikonal quasinormal modes, and modify deflection angles in static spherically symmetric backgrounds.
-
Probing Effective Field Theory Corrections with Quasinormal Modes and Gravitational Lensing in Reissner-Nordstr\"om Black Holes
Derives EFT corrections to deflection angle, photon sphere radius, critical impact parameter, and strong lensing coefficients for Reissner-Nordström black holes in weak and strong deflection regimes.
-
Shadow dependent phenomenology framework for rotating black hole metric
A diffeomorphic inversion re-parameterizes Kerr, Kerr-MOG, and Horndeski black hole observables in terms of the shadow radius, yielding model-specific deflection and luminosity scalings that break mass degeneracy.
-
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.