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As $g_{\mu\nu}$ can be taken to be symmetric, it contains 10 functions of spacetime in 4 dimensions. But, why we call these 10 functions as the degrees of freedom of the metric while they are the functions of only 4 spacetime variables?

What is meant by "degrees of freedom" here?

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  • $\begingroup$ might be a sort of duplicate:math.stackexchange.com/q/612159 $\endgroup$
    – user81619
    Commented Sep 1, 2015 at 19:45
  • $\begingroup$ I have already checked the link before posting the question, my question is not about how many DOFs rather why are they DOFs? $\endgroup$
    – Archimedes
    Commented Sep 1, 2015 at 19:53
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    $\begingroup$ Because the 4 spacetime variables are just labels, and at each set of values of the labels you assign the 10 values of the degrees of freedom (which vary rather freely). $\endgroup$
    – Sebastian Riese
    Commented Sep 1, 2015 at 19:55

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