# What is a vacuum?

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1. Mar 6, 2015

### Mentz114

This metric $ds^2=\frac{K}{r}\left(-dt^2+dr^2+r^2d\phi^2+r^2\sin(\theta)^2d\theta^2 \right)$ (obviously in a spherical polar chart) gives an Einstein tensor (in the comoving frame field)

$\kappa T_{00}=\frac{3\,K}{4\,r},\ \kappa T_{11}=-\frac{5\,K}{4\,r}, \ \kappa T_{22}=\frac{K}{4\,r}, \ \kappa T_{33}=\frac{K}{4\,r}$

The Weyl curvature is zero ( conformal flatness ).

This is not a vacuum but the trace ${T^\mu}_\mu$ is zero. Is this a spherically symmetric radiation filled universe with some extra something happening in the $r$-direction ?

Presumably for this to exist there must be a point source ?