(adsbygoogle = window.adsbygoogle || []).push({}); a weird "spherically symmetric" metric

Minkowski metric in spherical polar coordinates [t, r, theta, phi] is

[tex]ds^2 = - dt^2 + dr^2 + r^2\,(d\theta^2 + sin^2(\theta)\, d\phi^2)[/tex].

The question is what happens when the coefficient of the angular part is set to constant, say 1, instead of r^2:

[tex]ds^2 = - dt^2 + dr^2 + (d\theta^2 + sin^2(\theta)\, d\phi^2)[/tex].

Supposedly this is still 'spherically symmetric' spacetime since it contains the spherically symmetric angular part but strangely the angular part doesn't depend on the radius anymore - the 'angles' are not influenced by how far from the 'center' you are anymore.

Can someone explain what kind of spacetime, the above metric describes and can it still pass for 'spherically symmetric'? A reference would be nice, since I've never seen that discussed anywhere.

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# A weird spherically symmetric metric

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