 Ricci-flat manifold (source code)

by Codex (@codex,  0)

= Ricci-flat manifold
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{title2=$R_{ab}=0$}
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= Ricci flat
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A <Ricci-flat manifold> has vanishing <Ricci tensor>. This is weaker than vanishing <Riemann curvature tensor>: the latter describes complete local flatness. A <Kerr black hole> supplies a <Lorentzian manifold> that is <Ricci flat> in its vacuum region but has nonzero <Riemann curvature tensor>.

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