An Einstein tensor is defined by
 |
where 
is the Ricci curvature tensor, 
is the scalar curvature,
and 
is the metric tensor. (Wald 1984, pp. 40-41).
It satisfies
 |
(Misner et al. 1973, p. 222).
Einstein Tensor
See also
Metric Tensor, Ricci Curvature Tensor, Scalar CurvatureExplore with Wolfram|Alpha
References
Misner, C. W.; Thorne, K. S.; and Wheeler, J. A. Gravitation. San Francisco: W. H. Freeman, 1973.Parker, L. and Christensen, S. M. "The Ricci, Einstein, and Weyl Tensors." §2.7.1 in MathTensor: A System for Doing Tensor Analysis by Computer. Reading, MA: Addison-Wesley, pp. 30-32, 1994.Wald, R. M. General Relativity. Chicago, IL: University of Chicago Press, 1984.Referenced on Wolfram|Alpha
Einstein TensorCite this as:
Weisstein, Eric W. "Einstein Tensor." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/EinsteinTensor.html