- #1
Vrbic
- 407
- 18
Homework Statement
It is not a homework but I'm interested in. How to show, very often used, ##p_t=-E##
Homework Equations
##p^{\mu}p_{\mu}=-1##
##H=\sum{p_i \dot{q}^i}-L##
##2L=u^{\mu}u_{\mu}##
##p_{\mu}=g_{\mu\nu}\dot{q}^{\nu}##
The Attempt at a Solution
##H=1/2(g^{\mu\nu}p_{\nu})=1/2(g^{\mu t}p_t^2+g^{\mu r}p_r^2+g^{\mu \theta}p_\theta^2+g^{\mu \phi}p_\phi^2)##. I suppose that ##H=E## and ##p_\theta=p_\phi=0## when ##r\rightarrow \infty##. But it is probably wrong way...there are squares.
Can you advice please?