Why torsion free metric compatible connection ?

1. Nov 20, 2007

smallphi

why torsion free metric compatible connection ???

Why in conventional GR we choose a torsion free, metric compatible connection?

Can that be derived from somewhere like physical principles/postulates or it's just a the simplest convenient choice (many terms drop from equations) that produces theory in agreement with experiment?

Had we chosen a connection with torsion that is not metric compatible, would that violate any experiment?

Also comment if you can on the Palatini's 'derivation' of the metric compatible torsion free connection by varying the connection in the action as a free field. Is that a real proof that the connection must be of this type or it's just an 'interesting fact' you can derive it that way?

Last edited: Nov 20, 2007
2. Nov 20, 2007

robphy

3. Nov 21, 2007

smallphi

What is the physical meaning of 'metric compatible' connection if any?

Wald says that metric compatible connection preserves the angle between two parallel transported 4-vectors. How is that relevant to physical experiments? What I am asking for is, can the metric compatibility or the lack of it be checked experimentally?

4. Nov 21, 2007

robphy

One view is that
"[torsion-free] metric compatibility" means that the metric tensor field carries all of the information of the geometry of spacetime....
Physically, this means that the metric tensor field determines the motion of free particles (the geodesic structure) and the propagation of light (the conformal structure..and causal structure).

This might be a useful resource:
http://relativity.livingreviews.org/open?pubNo=lrr-2004-2&page=articlesu3.html [Broken]

Last edited by a moderator: May 3, 2017