I have been recently working with Schwarzchild's solution:(adsbygoogle = window.adsbygoogle || []).push({});

ds^{2}= - (1- (2GM/rc^{2}))c^{2}dt^{2}+ dr^{2}/(1-2GM/rc^{2}) + r^{2}(dθ^{2}+ sin^{2}(θ)d∅^{2})

Now, when deriving the various general relativistic tensors for this metric such as the Ricci tensor, I found the calculations to be painfully tedious and monstrous (but not impossible). As I did these calculations, I thought about the fact that I was essentially working to derive a stress energy momentum tensor that I (with my current interpretation of the tensor) would probably not get as much information from as I should.

After all, I remembered how I derived the stress energy momentum tensor for the Morris-Thorne wormhole and then didn't fully know what that tensor implied.

I know the supposed meanings of the individual elements of the tensor. For instance, I know that T_{00}is energy density while the rest of this row and column are energy flux. Every other element is momentum flux.

As you can see, I know this part.

However, there is more to it than this. For example:

We know that the Schwarzchild metric describes the space-time geometry around a spherical, non-electrically charged, non-rotating body. The stress energy momentum tensor however, does not have an element that tells you the shape of the body or system that generates the space-time curvature, nor does it tell you that it is static or non-rotating or non-electrically charged (although that last one can be inferred based on the fact that there are no electromagnetic terms in the derivation of this metric).

How exactly did Einstein get this information? How does one know from a metric what shape the body is or whether or not it is rotating (and other information like this)?

I have one hypothesis about this, and that is the fact that this metric is in a spherical basis. If that is not it, then please tell me where one gets this information.

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# How did Einstein derive the meaning of Schwarzchild's metric

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