# Is there a 'correct frame' in general relativity?

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?

• 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. – Omry Mar 19 '17 at 4:33