# Schwarzschild metric

1. Apr 21, 2005

### JohanL

Light rays in the schwarzschild metric satisfy the differential equation

$$\frac {d^2u} {d\phi^2}+u=3Mu^2$$

u=1/r

I want to show that there is closed orbits with constant radius and also calculate the radius of the orbits as a function of the Schwarzchild radius.
Can anyone help me with this? Or give me some hits?
As simple as possible plz.

2. Apr 21, 2005

### pervect

Staff Emeritus

Well, if the orbit is one of constant radius, then du/dphi must be equal to zero, and so must du^2/dphi^2.

You are then left with the equation u = 3Mu^2. Solve for u.