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I Conserved quantities in GR

  1. Nov 18, 2017 #1
    Hello! I am reading about spherical geometry and for a static system and based on the metric, ##p_0## and ##p_\phi## are constant of motion. I am not sure I understand in which sense are they constant? The energy of a particle measured by an observer depends on the metric (so on its position) in space. So ##p_0## is not the energy of the particle (can't even be measured I think). Can someone explain this to me a bit more? Thank you!
     
  2. jcsd
  3. Nov 18, 2017 #2

    PeterDonis

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    2016 Award

    Staff: Mentor

    From what source? Please give a specific reference.

    They are constants of geodesic motion.

    "Constant" means "does not change".

    No, it doesn't. It depends on the 4-momentum of the particle and the 4-velocity of the observer.

    Not the energy measured by an observer that is (momentarily) co-located with the particle, no--at least, assuming the observer and the particle are not at infinity.

    Yes, it can, but it's not as straightforward as an observer co-located just measuring the particle's energy.

    It would help greatly if you would give a specific reference and show some math. You should particularly focus on the actual mathematical expression for ##p_0##. What quantities occur in it? What do those quantities mean?
     
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