The stress-energy-momentum tensor in GR, has components that vary according to velocity (ex: the top left most energy density component)

depending on your frame of reference (i.e. relative velocity with respect to some point in space) the energy density at that point could be wildly different, as I believe it is given by $ \frac{E_{rel}}{c^2} $

This surprises me, since it means one observer could see a point in spacetime to be wildy energy-dense, another not-so-much, and that could lead to either:

  1. inconsistent curvatures
  2. OR inconsistent constants (i.e. despite measuring difference stress-energy-momenta tensors they still ended up with the same curvature but the constants relationship MUST then be different)

This can't be avoided unless there is a notion of a proper frame of reference for each point in space time. Which also feels wrong. Where am I going wrong here?

  • $\begingroup$ The same occurs for the energy-momentum tensor in SR. Lorentz boosts suffice to change the energy-momentum tensor, and, simpler still, change the four-momentum. $\endgroup$ – Omry Mar 19 '17 at 4:33

It might be unsettling, but no there is no such preferred frame of reference. But you can still check which quantities are actually invariant constants under change of frame.

  • $\begingroup$ So if I identify some object in space say a rock that weights 1 kg, but i'm moving very very close to the speed of light away from it, then I could interpret it as having extremely high energy density (and if its in motion then very high momentum flux for that matter). To take it to an extreme, I might even measure said rock, to exceed the density required to form an event horizon around it, yet someone else near the rock and in a similar frame as the rock would just see a regular old rock. This is very strange! $\endgroup$ – frogeyedpeas Mar 19 '17 at 4:49
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    $\begingroup$ That's a problem you should be able to just write down the stress energy for and see it transform. It's a good exercise. $\endgroup$ – AHusain Mar 19 '17 at 4:52
  • $\begingroup$ Hmm let me check this out actually then $\endgroup$ – frogeyedpeas Mar 19 '17 at 4:54

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