I'm writing a paper about the motion of photons near a Schwarzschild black hole. At some point there's a derivative of the Hamiltonian of the system with respect to time $\tau$. I need to explain what the proper time is $\tau$, but it's quite odd because photons don't have any proper time.
The Hamiltonian that I have is
$$H = - \left( 1-\frac{2M}{r} \right)^{-1} \frac{p_{t}^2}{2}+\left( 1-\frac{2M}{r} \right) \frac{p_{r}^2}{2}+\left( \frac{p_{ \theta}^2}{2r^2}+\frac{p_{\phi}^2}{2r^2sin^2\theta} \right).$$
- So what would be the definition in this case?
- "the proper time is the time for the photon although he doesn't have one?"
Does anyone know?
No comments:
Post a Comment