Every time I try to find the answer to this question I get redirected to different pages that ultimately do not end up answering my question. I have some understanding of Riemannian geometry but have no idea how to link it to the presence of a mass with Einstein's field equation.

Could someone provide an example, either linked or typed and submitted as answer, of a simple question with an object of defined mass?

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    $\begingroup$ Have you looked at any textbooks on general relativity? $\endgroup$
    – hft
    Mar 5 '15 at 19:58
  • $\begingroup$ Possible duplicate: physics.stackexchange.com/q/127132/2451 Possible duplicate by OP: physics.stackexchange.com/q/168222/2451 $\endgroup$
    – Qmechanic
    Mar 5 '15 at 19:58
  • $\begingroup$ I have greater understanding of the mathematics than the user who asked that and would like answers that go more in-depth into the mathematics starting at where my understanding stops rather than getting a full introduction into tensors. $\endgroup$ Mar 5 '15 at 20:06
  • $\begingroup$ I haven't been able to get any textbooks on the subject, but I have watched online lectures. These acted as a good introduction into the mathematics but didn't explain how to use the equations to calculate a real gravitational field $\endgroup$ Mar 5 '15 at 20:07
  • $\begingroup$ As for whether or not this question has been asked before: I have asked it again because all similar questions either different enough as to not match my curiosity or did not have adequate answers. To fix the latter issue I have tried to word my question in such a way that I would get the answer to my question and no misinterpretations. $\endgroup$ Mar 5 '15 at 20:19

As I answered to the linked question, it is almost never the case that we write out the field equations in full then work through some procedure to solve them. I think you will struggle to find any reference that does this. Solutions are almost invariably found by exploiting symmetry or using approximations such as the weak field.

Have you Googled for the derivation of the Schwarzschild metric? There must be a thousand articles out there explaining how this is done, and it's the simplest case I know of. Other obvious starting points would be the derivation of the FLRW metric and the Kerr metric.


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