Applications of the Gauss-Bonnet theorem to gravitational lensing

Details Applications of the Gauss-Bonnet theorem to gravitational lensing Applications of the Gauss-Bonnet theorem to gravitational lensing

2008-07-05

arxiv.org/abs/0807.0854v1

Class.Quant.Grav.25:235009,2008

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

10 pages, 1 figure, IoP style

Scientific paper

10.1088/0264-9381/25/23/235009

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.

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