Intrinsic property of spacetime ?

[Worldline]

Hi friends

what are intrinsic properties of spacetime ?
curvature & torsion ? or they are just properties of connections ?
Since in teleparallel gravity we consider them as properties of connections.

thank u

 

[pervect]

Well, the Lorentz interval is obviously a property of space-time, and that gives us a metric.

What we need to go on to get a connection and curvature from the metric is parallel transport.

Reading the fine print in Wald, though, it's not terribly clear if you can get parallel transport from the metric in the way I'm used to in the presence of torsion. So I can answer the first part fairly confidently, I think - space-time gives you the Lorentz interval and the metric.

But I'm not sure , in the presence of torsion, what it takes to go from the metric to parallel transport (which gives you connections and curvature.) At the moment I'm suspecting it does not, but I might be seriously confused. I opened a different thread so I don't export any confusion into this one.

Without torsion, I know it is possible to single out a connection from a metric.

 

[Worldline]

Thank pervect
i am a bit confused !
i think that i need more study !