What is Spherically Symmetric Radiation-Filled Universe?

[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 ?

Any clarifications, please ?

 

[Mentz114]

Since posting this I've had time to do some reading and I have mistaken the EMT for something it is not.All the radiation metrics use a null coordinate.

This EMT is not anything physical. Whoops.