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Vacuum solution (general relativity)
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<p>In <a href="/facts/General_relativity/jVsoIg8X">general relativity</a>, a vacuum solution is a <a href="/facts/Lorentzian_manifold/VFXsVjqb">Lorentzian manifold</a> whose <a href="/facts/Einstein_tensor/ejyGdaFz">Einstein tensor</a> vanishes identically. According to the <a href="/facts/Einstein_field_equation/j2rJTzW9">Einstein field equation</a>, this means that the <a href="/facts/Stress%25E2%2580%2593energy_tensor/wWKrzjfI">stress–energy tensor</a> also vanishes identically, so that no matter or non-gravitational fields are present. These are distinct from the <a href="/facts/Electrovacuum_solution/DFTEpTjd">electrovacuum solutions</a>, which take into account the <a href="/facts/Electromagnetic_field/MacraS8y">electromagnetic field</a> in addition to the gravitational field. Vacuum solutions are also distinct from the <a href="/facts/Lambdavacuum_solution/L9Crz4Eg">lambdavacuum solutions</a>, where the only term in the stress–energy tensor is the <a href="/facts/Cosmological_constant/bjMksSA2">cosmological constant</a> term (and thus, the lambdavacuums can be taken as cosmological models). </p><p>More generally, a vacuum region in a Lorentzian manifold is a region in which the Einstein tensor vanishes. </p><p>Vacuum solutions are a special case of the more general <a href="/facts/Exact_solutions_in_general_relativity/MFb3MFaC">exact solutions in general relativity</a>. </p>