This is based on the metric of the surface of a 3D sphere. A and B are constants with dimension (length)^2. Coordinates are(adsbygoogle = window.adsbygoogle || []).push({});

[tex] x^0 = t, x^1 = \theta, x^2 = \phi[/tex]

[tex]ds^2 = -c^2AB^{-1}dt^2 + Bd\theta^2 + Bsin^2(\theta)d\phi^2[/tex]

It satisfies the Einstein field equations with only one component of the energy-momentum tensor non-zero -

[tex]T^{00} = \frac{c^2A}{B^2}[/tex]

The curvature scalar is

[tex]R^\mu_{ \mu} = \frac{2}{B}[/tex]

This looks like a two-dimensional static cosmos with constant curvature ( radius sqrt(B)) and total energy A, and no energy currents.

Is this a viable interpretation ?

[ Assuming I haven't made any gross errors in the calculation...]

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# Is this line element known to anyone ?

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