Is it theoretically possible that the metric in the whole universe would be described(adsbygoogle = window.adsbygoogle || []).push({});

by Kruskal extension of Schwarzschild solution of Einstein equation and in the universe

would be no matter at all (vaccum solution everywhere).

What's the interpretation of parameter m characterising Schwarzschild solution in this case?

Does the matter need to be somewhere in the universe in case of this solution

because we don't want to have white hole? Are there also other arguments for

placing matter in some regions.

What about the statement that matter (stress energy tensor) is the source of

gravitational field. Are nonflat global solution of vaccum Einstein equation acceptable

in whole universe (theoretically) or if there was vaccum everywhere in the universe

it would have to be flat.

Thanks.

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# Schwarzschild solution without matter

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