Vacuum Solution (General Relativity)
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High Quality Content by WIKIPEDIA articles! In general relativity, a vacuum solution is a Lorentzian manifold whose Einstein tensor vanishes identically. According to the Einstein field equation, this means that the stress-energy tensor also vanishes identically, so that no matter or non-gravitational fields are present. More generally, a vacuum region in a Lorentzian manifold is a region in which the Einstein tensor vanishes. It is a mathematical fact that the Einstein tensor vanishes if and only if the Ricci tensor vanishes. This follows from the fact that these two second rank tensors stand...
High Quality Content by WIKIPEDIA articles! In general relativity, a vacuum solution is a Lorentzian manifold whose Einstein tensor vanishes identically. According to the Einstein field equation, this means that the stress-energy tensor also vanishes identically, so that no matter or non-gravitational fields are present. More generally, a vacuum region in a Lorentzian manifold is a region in which the Einstein tensor vanishes. It is a mathematical fact that the Einstein tensor vanishes if and only if the Ricci tensor vanishes. This follows from the fact that these two second rank tensors stand in a kind of dual relationship.
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