A way one counts degrees of freedom(i.e. independent entries of the metric tensor ) in General Relativity is this: one goes to the linearized version, vacuum solution, and he sees that there are two independent polarizations(e.g. L-R).

  1. First: how can I know that the number of degrees of freedom in the linearized case are the same of the general case?

  2. Second: I want to know in general how can I interpret physically the degrees of freedom? Or have I to see it for each system under investigation?

  3. Third, is there other ways to count degrees of freedom? For example by Killing Vectors?

  • $\begingroup$ This question (v3) is also addressed in e.g this and this Phys.SE answers. $\endgroup$ – Qmechanic Oct 2 '16 at 17:57

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