# Timelike Geodesics Crossing u=0 in Kruskal-Szekeres

1. Nov 25, 2012

### Airsteve0

In a problem sessions for my general relativity course we examined the red-shift for a light signal passed from an emitter to an observer as they both cross u=0 (r=2m) in the Kruskal Szekeres diagram. We were able to reduce the equation for the red-shift to what is shown below in (1) and then further reasoning was done to give what is shown in (2). However, I am unsure of how the (r')'s changed to gammas and was wondering if someone understands how this was done. Additionally, my professor left it as an exercise to further reduce the $\frac{v_o}{v_e}$, and I am not sure how to manipulate these, any ideas? Thanks in advance for any insight!

(1) $(1+z)\propto\frac{\dot{r_e}}{\dot{r_o}}\frac{v_o}{v_e}$

(2) $(1+z)\propto\frac{\gamma_e}{\gamma_o}\frac{v_o}{v_e}$