Back

Gravitational Lensing

I will reuse equation for energy from the geodesics chapter:

E2=(drdλ)2+L2r2−2L2r3+2rϵ−ϵ.\mathcal{E}^2 = \left(\frac{dr}{d\lambda}\right)^2 + \frac{\mathcal{L}^2}{r^2} - \frac{2\mathcal{L}^2}{r^3} + \frac{2}{r} \epsilon - \epsilon.

We are considering the path of light rays (ϵ=0\epsilon = 0)

E2=(drdλ)2+L2r2−2L2r3.\mathcal{E}^2 = \left(\frac{dr}{d\lambda}\right)^2 + \frac{\mathcal{L}^2}{r^2} - \frac{2\mathcal{L}^2}{r^3}.