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I am speaking about GR with classical fields and energy. One question spread over three increasingly strict situations: Is there an energy density limit in GR? (literally can the energy density ...

 

I have been studying a bit of GR and am still a bit confused as how it works with perturbations of the metric or even in what norm the perturbation is meant to be understood. For example what hap...

 

Total derivatives in GR Ask Question Asked 10 years 4 months ago Modified 10 years 4 months ago

 

4) Fundamentally the superscripting and subscripting is designed to keep track of what basis or bases you are using. In a lot of standard linear algebra the basis and dual basis coincide hence there is no need to use upper and lower indices. In GR you do not have that simplicity hence the need for the upper and lower indexing.

 

Often students have difficulty reconciling the General Relativity (GR) view of gravity versus their own experience with gravity on the surface of Earth.

 

Another possibility is that in SR we are obliged to make only Lorentz transformations. But in GR we can do whatever coordinate transformations we want so the transformation above should be allowed.

 

? ? $\lambda$ can be any affine parameter. For an interesting discussion of this read the answers to What is the physical meaning of the affine parameter for null geodesic? However coordinate time is not an affine parameter. You can rewrite the geodesic equation using coordinate time by using the chain rule but as mentioned in Qmechanic's answer this introduces an extra term:

 

What is the correspondence between the conserved canonical energy-momentum tensor which is $$ T^{\\mu\\nu}_{can} := \\sum_{i=1}^N\\frac{\\delta\\mathcal{L}_{Matter ...

 

I've been wondering for a while why the notion of covariance in GR is so important. I have some background in mathematical physics so I know the difference between co- and contravariant components of a tensor a such. Hi Dimitri - General relativity requires that the laws of physics are the same in all coordinate systems.

 

Correct me if I'm wrong. But my understanding is the following. Introducing a tetrad means introducing an orthonormal basis of smooth vector fields...