- #1

kleinwolf

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1) gravitational field equivalent to acceleration => curvature (due to local lorentz contraction)

2) gravitational field is equiv. to energy => curvature has to be linked non-linearly to the energy, which is the 00 element of the stress-energy tensor.

Einstein then uses the work of Cartan-Riemann about the curvature tensor, and the Ricci tensor R_ij.

However, the obtention of the curvature tensor is based on the use of closed loops (for the use of the Stokes theorem in the version I saw) :

the curvature is defined with the parallel displacement of a vector along a closed loop.

My question is : Is this physically acceptable, since in GR a loop means a loop in space-time, hence coming back in time ?

This is then not surprising that Goedel found solutions to Einstein's equations in which timelike loops exist.