There seems to be an emphasis in several books on general relativity that the metric (components) in itself does not reflect anything physical, only our choice of coordinates. On the other hand it can seem like the authors, instead of being true to this, treat the metric (components) as containing physical information.(adsbygoogle = window.adsbygoogle || []).push({});

For example in deriving the Schwarzschild solution one makes some symmetry arguments to restrict the form of the metric (components) and thereby solving the Einstein equations for empty space and thus ending up with this famous solution.

Since the Einstein equations are now solved for a vacuum one would think that the only reason we did not get a flat-space solution was due to the symmetry assumptions put in at the start of the derivation.

But is this really a physical assumption at all? Like the authors emphasizing the nonphysical nature of metric (components) I would think that one could reach the assumed form just by choosing a certain basis. But if this is not a physical assumption we have not put any physical information in except that the Einstein equations are to be solved for a vacuum, so then it would be reasonable to expect all solutions consistent with a vacuum (T=0).

So where does the assumption of a central mass lie in the Schwarzschild solution, and if it actually does lie in the assumption of the form of the metric how is this reconciled with the fact that the metric (only?) reflects choice of coordinates?

Edit: (components).

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# Solving field equations and the nonphysical nature of the metric. (GR)

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