Applications of the Gauss–Bonnet theorem to gravitational lensing

By G. W. Gibbons, M. Werner. 2008

351 citations recorded by the source corpus.

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.

Subfields: Astronomy and Astrophysics

View Paper: https://www.semanticscholar.org/paper/7859582e59b59cea1a5e2be00eb5612cfd1e4693

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In Astronomy and Astrophysics

1. A. Ovgun
2. K. Jusufi
3. M. Werner
4. Mert Okyay
5. M. Jamil
6. Qiang Wu
7. Tao Zhu
8. Carlos A. R. Herdeiro

Citations in the corpus

• Shadows and deflection angle of charged and slowly rotating black holes in Einstein-Æther theory (2019, methodology): “By construction, there are two corresponding jump angles in the limit R →∞, namely the following condition is recovered θO + θS → π [57].”
• Nonlinear electrodynamics effects on the black hole shadow, deflection angle, quasinormal modes and greybody factors (2021, methodology): “[64] K. Jusufi, M. C. Werner, A. Banerjee and A. Övgün, “Light Deflection by a Rotating Global Monopole Spacetime,” Phys.”
• Stationary Metrics and Optical Zermelo-Randers-Finsler Geometry (2008, methodology): “One may use the Gauss-Bonnet Theorem and information about the curvature of the optical metric to make general statements about light bending [2, 3, 4] and one may use the Projective Geometry to illuminate the dependence of light bending on the cosmological constant [5].”
• Gravitational lensing in the Kerr-Randers optical geometry (2012, methodology): “4 Application to gravitational lensing Having constructed the osculating Riemannian manifold (SR, ḡ) with boundary ∂SR = γḡ ∪ CR as described in the previous section, we can now apply the Gauss-Bonnet method [9] to evaluate the asymptotic light deflection angle.”