= Vacuum spacetime
{title2=$T_{ab}=0$}
A <vacuum spacetime> has vanishing matter <stress-energy tensor>. In $D>2$ dimensions, tracing the <Vacuum Einstein equations> gives $R=2D\Lambda/(D-2)$ and hence $R_{ab}=2\Lambda g_{ab}/(D-2)$; in four dimensions this reduces to $R_{ab}=\Lambda g_{ab}$. With zero <cosmological constant> it is <Ricci flat>, although its full <Riemann curvature tensor> can be nonzero: a vacuum <Kerr black hole> and vacuum <gravitational waves> illustrate that distinction.
Back to article page
