Sunday, December 29, 2019

general relativity - How to define the proper time of a photon?


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=(12Mr)1p2t2+(12Mr)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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