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 τ. I need to explain what the proper time is τ, but it's quite odd because photons don't have any proper time.
The Hamiltonian that I have is
H=−(1−2Mr)−1p2t2+(1−2Mr)p2r2+(p2θ2r2+p2ϕ2r2sin2θ).
- 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?
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