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How would one calculate angle of deflection in case of gravitational lensing on galaxy cluster with given potential?

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Gravitational potential of galaxy cluster is given as

\[h_{00} = \frac{a}{\sqrt{1+\left(\frac{r}{r_0}\right)^2}}\]

and conditions are such that we can determine: \(a = \frac{2GM}{c^2r_0}, r_0 = \frac{1}{\sqrt{3}}Mpc\). M is mass of cluster.

When \(r>>r_0\), potential becomes that of a point mass \(h_{00}\rightarrow \frac{2GM}{c^2r}\), so I tried to use derivation for that but I'm not sure it is the right way and calculations quickly become very complicated for given potential.

So my question is: how can I calculate angle of deflection of photon moving at a distance d from cluster in case of such potential ?

asked Jan 7, 2016 in Astronomy by Ivana [ no revision ]

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