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Ricci scalar

by alejandrito29
Tags: ricci, scalar
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alejandrito29
#1
Jun10-10, 05:06 PM
P: 143
i need examplees where the ricci scalar is constant but nonzero . Particulary i search examples of line element.

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nicksauce
#2
Jun10-10, 06:13 PM
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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
#3
Jun10-10, 06:17 PM
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Minowski space should have a constant Ricci scalar, right? But it is zero, from what I gather.

nicksauce
#4
Jun10-10, 06:39 PM
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Ricci scalar

Quote Quote by espen180 View Post
Minowski space should have a constant Ricci scalar, right? But it is zero, from what I gather.
Yup.
George Jones
#5
Jun10-10, 06:47 PM
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de Sitter spacetime and anti-de Sitter spacetime.


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