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If we imagine a lightwave moving through space without considering how the space is deformed due to the energy and momentum of the light, we would find it redshifted once we take GR into account correct?

Is it then correct that if we instead had a massive particle moving through space without taking GR into account, we would find it moving more slowly once we take GR into account?

I'm considering a universe that is flat and empty apart from this one particle and the deformation in the spacetime it causes.

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  • $\begingroup$ "I'm considering a universe that is flat and empty apart from this one particle and the deformation in the spacetime it causes" If there is only one particle in the universe what gave it the momentum to move? contradictory initial terms. $\endgroup$
    – anna v
    Commented Sep 28, 2020 at 18:20
  • $\begingroup$ So you think that the derivation of the Schwarzschild metric, for example, is incorrect and not worth discussing because if a black hole is the only thing in the universe... then what gave it the mass to exist? $\endgroup$
    – Quanta
    Commented Sep 28, 2020 at 19:28
  • $\begingroup$ One expects the law of conservation of momentum to hold, whereas there is no law of mass conservation, even logically, relative to what (0,0,0) would it be moving? $\endgroup$
    – anna v
    Commented Sep 29, 2020 at 4:07

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If by "taking GR into account" you mean placing the particle into an expanding space-time such as in the standard cosmological model, then yes. The cosmological constant acts as a repulsive potential and thus a decelerating force w.r.t. to a particle moving towards you.

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