If this turns out to admit a stress energy tensor such that the resulting model satisfies the Einstein field equation ( say, for a static spherically symmetric perfect fluid obeying suitable energy conditions and other properties expected of reasonable perfect fluid ), then, with appropriate tensor fields representing physical quantities such as matter and momentum densities, we have a piece of a possibly larger spacetime; a piece which can be considered a " local solution " of the Einstein field equation.
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If this turns out to admit a stress energy tensor such that the resulting model satisfies the Einstein field equation ( say, for a static spherically symmetric perfect fluid obeying suitable energy conditions and other properties expected of reasonable perfect fluid ), then, with appropriate tensor fields representing physical quantities such as matter and momentum densities, we have a piece of a possibly larger spacetime; a piece which can be considered a " local solution " of the Einstein field equation.
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