A GR Unphysical Aspects: Time Protection Hypothesis & Riemannian Curvature

[jk22]

As history is Newton considered infinite speeds of his gravitational force as unphysical, out of which Einstein constructed relativity.

In special relativity moving faster than c induces an imaginary space-time and is hence ruled out.

My question is regardin towards GR, in which Gödel showed that in rotating universes solutions to GR closed time-like loops could exist.

Are those also ruled out by physics community due to the time protection hypothesis ?

I suppose yes. Then by looking at the construction of GR, is it that the construction of the Riemannian curvature transport is made out of parallel transporting a vector along a closed curve ?

This seems unphysical to build a theory out of closed loops in space-time.

So how could other calculations of the curvature be made on helix-like curves ? I'm looking for documents about this particular point.

Thanks.

 

[PAllen]

To define the curvature tensor completely, you must use curves that have nothing to do with histories of particles, e.g. spacelike curves, and curves that mix timelike and spacelike, including having sections with different time orientations. This has nothing whatsoever to do with whether the manifold admits closed timelike curves.

As to whether CTCs are unphysical, that is ultimately a matter of opinion. I think they are, others will disagree.

 

[PeterDonis]

by looking at the construction of GR, is it that the construction of the Riemannian curvature transport is made out of parallel transporting a vector along a closed curve ?

A closed curve, but not a closed timelike curve. The closed curve will not be timelike everywhere. In fact it won't even have to be a smooth curve; the typical examples used in GR textbooks are closed loops composed of distinct segments, which are not smooth at the corners where different segments meet.

 

[robphy]

Then by looking at the construction of GR, is it that the construction of the Riemannian curvature transport is made out of parallel transporting a vector along a closed curve ?

This seems unphysical to build a theory out of closed loops in space-time.

Another approach could probably be taken to define the Riemann curvature.
Rather than thinking about parallel-transport around a loop,
think about parallel-transporting from event A to event B along two different paths.

In classical mechanics, the analogue is
rather than computing the work done around a loop,
compute the work done from point A to point B along two different paths.