Finding Ricci Scalar Constant Nonzero Line Elements

[alejandrito29]

i need examplees where the ricci scalar is constant but nonzero . Particulary i search examples of line element.

Pd: this is not a homework,

 

[nicksauce]

I'm not sure if you are referring to spaces or spacetimes. If spaces, then maximally symmetric spaces have the property that the Ricci scalar is constant everywhere. In 3 dimensions these are the 3-sphere and the 3-hyperboloid (and Euclidean space, but there R=0). If you are referring to spacetimes, then the Ricci scalar is proportional to the trace of the stress tensor (T), so you need to find some spacetime with constant T everywhere. I can't think of any examples of the top of my head.

 

[espen180]

Minowski space should have a constant Ricci scalar, right? But it is zero, from what I gather.

 

[nicksauce]

Minowski space should have a constant Ricci scalar, right? But it is zero, from what I gather.

Yup.

 

[George Jones]

de Sitter spacetime and anti-de Sitter spacetime.