# GR conditions conserved quantities AdS s-t; t-l geodesic

1. May 21, 2017

### binbagsss

1. The problem statement, all variables and given/known data

Question attached

2. Relevant equations

3. The attempt at a solution

part a) $ds^2=\frac{R^2}{z^2}(-dt^2+dy^2+dx^2+dz^2)$
part b) it is clear there is a conserved quantity associated with $t,y,x$

From Euler-Lagrange equations $\dot{t}=k$ , k a constant ; similar for $\dot{y}=c$ and $\dot{x}=b$ , $b,c$ constants

I get the Lagrangian as $L=\frac{R^2}{z^2}( \dot{x^2} + \dot{y^2} + \dot{z^2} - \dot{t^2} )$

Let me combine all the constants as $\kappa$ then I can write this as:

$\frac{R^2}{z^2}( \kappa + \dot{z^2} )<0$ ; since $L$ must be $<0$ for a time-like geodesic. I'm not sure what to do now...

2. May 26, 2017

### PF_Help_Bot

Thanks for the thread! This is an automated courtesy bump. Sorry you aren't generating responses at the moment. Do you have any further information, come to any new conclusions or is it possible to reword the post? The more details the better.

3. May 27, 2017

### binbagsss

my pockets are all empty, ta bot bruv' though