# Can massless particles reach the boundary at z=0?

1. Dec 5, 2016

### Poirot

1. The problem statement, all variables and given/known data
We're working in 2-d Anti-de Sitter space with metric: \begin{eqnarray*}ds^2 = \frac{1}{z^2}(-dt^2 + dz^2)\end{eqnarray*} with 0<=z.

The solution is: \begin{eqnarray*}z^2 = (t+c)^2 + B\end{eqnarray*} And we've been asked to plot this (I think its a parabola with minima at t=-c, z=(B)1/2 (told that B>0). (I'm not sure if the c in this case is the speed of light or just a constant, it hasn't been said)
The last part asks if massless particles can reach the boundary z=0?

2. Relevant equations

3. The attempt at a solution
I don't really understand this to be honest. I know that the geodesic L=0 for massless particles but I don't really know the physics implications for a massless particle. I assume it's to do with the fact that massless particles travel at the speed of light so perhaps theres a consequence at the boundary?

Thanks for any help, I'm a little confused!

2. Dec 10, 2016