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Applications of the Gauss-Bonnet theorem to gravitational lensing · Around

2008

Applications of the Gauss-Bonnet theorem to gravitational lensing

Gibbons, G W, Werner, M C

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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.

Built on

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Bisnovatyi-Kogan G S and Zel’dovich Ya B 1969 Models of clusters of point masses with large central redshifts Astrophys
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Klingenberg W 1978 A Course in Differential Geometry
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Binney J and Tremaine S 1987 Galactic Dynamics
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