Space where General Reletivity Resides

[Philosophaie]

There are many spaces: Einstein-Cartan Space, Riemann Space, Minkowski Space... Which one does the Earth and the Sun reside in? Which one has Torsion, mass etc. if any?

 

[russ_watters]

Those are basically just geometrical representations. It could be said that we reside in none of them or all of them, depending on how one reads the question.

 

[Philosophaie]

A model can be formulated in say Riemann space to take in account for the magnetic and gravitational field of the sun. The torsion would be zero. The metric would be the Schwarzschild metric. Affinity would be the Christoffel symbol. Then the Riemann Curvature and Ricci Tensors can be calculated. Would this be the correct model for the sun?

 

[marcus]

There are many spaces: Einstein-Cartan Space, Riemann Space, Minkowski Space... Which one does the Earth and the Sun reside in? Which one has Torsion, mass etc. if any?

Russ has basically given the complete answer. I'll toss in my two bits.

You are listing alternative geometries, that go onto space and describe how it acts. Alternative geometries, not different spaces as such.

Maybe a trivial distinction but you probably know the quotes from Einstein where he says points in space have no physical existence, no objective reality.
So the thing to focus on is the geometry. Often it is a dynamic geometry able to interact with matter, behavior governed by a Lagrangian or a differential equation.

So what your question means to me is which is the best most realistic description of geometry and how it behaves interactively with matter?

I can't tell you any final answer but obviously Minkowski geometry is highly unrealistic. It is only right if there is no matter, and not always even then. It is only approximately right if there is negligible matter in the universe. It does not expand. It is flat. It sucks.

On the other hand (strictly interpreted) Riemannian geometry has the wrong metric signature---which Minkowski at least gets right! So Riemannian is no good.

As Russ hints, all these geometries are human constructs. So the question is which is the most realistic, not which do we live in.

Of the ones you listed I'd go with Einstein Cartan.

But I also like the new version of quantum geometry that came out in 2007. It looks like it might give classical GR in the large distance limit, and also be kind of interesting and weird in the very small distance limit.

 

[Philosophaie]

A model can be formulated in Einstein-Cartan Space would have to take into account spin and torsion of which I am unfamiliar in formulating. Any suggestions on how to learn about these modeling techniques of the sun?

 

[Orion1]

General Relativity...

Any suggestions on how to learn about these modeling techniques of the sun?

Use the Schwarzschild metric and the Tolman-Oppenheimer-Volkoff equation to model stars in astrophysics and General Relativity.

In Einstein's theory of general relativity, the Schwarzschild solution (or the Schwarzschild vacuum) describes the gravitational field outside a spherical, non-rotating mass such as a (non-rotating) star, planet, or black hole. It is also a good approximation to the gravitational field of a slowly rotating body like the Earth or Sun. The cosmological constant is assumed to equal zero.

In astrophysics, the Tolman-Oppenheimer-Volkoff (TOV) equation constrains the structure of a spherically symmetric body of isotropic material which is in static gravitational equilibrium, as modeled by General Relativity.

The extension of Riemannian geometry to include affine torsion is now known as Riemann–Cartan geometry.

While it is intuitively compelling that this implies Einstein–Cartan theory, the rigorous mathematical proof of convergence to the equations of Einstein–Cartan theory has not been done.

The equivalent TOV solution for the Einstein–Cartan theory, would be an interesting examination.

Reference:
http://en.wikipedia.org/wiki/Riemannian_geometry"
http://en.wikipedia.org/wiki/Schwarzschild_metric"
http://en.wikipedia.org/wiki/Tolman-Oppenheimer-Volkoff_equation"
http://en.wikipedia.org/wiki/Einstein%E2%80%93Cartan_theory"