Difference between revisions of "Cosmological constant"

From Diffgeom
Jump to: navigation, search
m (1 revision)
(Definition)
 
Line 7: Line 7:
 
where <math>R</math> denotes the [[Ricci curvature tensor]].
 
where <math>R</math> denotes the [[Ricci curvature tensor]].
  
Equivalently the cosmological constant for an Einstein metric can be defined as the [[Ricci curvature]] associated with any one-dimensional subspcae of the tangent space.
+
Equivalently the cosmological constant for an Einstein metric can be defined as the [[Ricci curvature]] associated with any one-dimensional subspace of the tangent space.

Latest revision as of 14:37, 18 May 2010

Definition

Let M be a manifold equipped with an Einstein metric. Then the cosmological constant of M is defined as the constant of proportionality \lambda for which:

R_{ij} = \lambda g_{ij}

where R denotes the Ricci curvature tensor.

Equivalently the cosmological constant for an Einstein metric can be defined as the Ricci curvature associated with any one-dimensional subspace of the tangent space.