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Scalar Curvature


The scalar curvature, also called the "curvature scalar" (e.g., Weinberg 1972, p. 135; Misner et al. 1973, p. 222) or "Ricci scalar," is given by

 R=g^(mukappa)R_(mukappa),

where g^(mukappa) is the metric tensor and R_(mukappa) is the Ricci curvature tensor.


See also

Curvature, Einstein Tensor, Gaussian Curvature, Mean Curvature, Metric Tensor, Radius of Curvature, Ricci Curvature Tensor, Riemann Tensor

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References

Misner, C. W.; Thorne, K. S.; and Wheeler, J. A. Gravitation. San Francisco: W. H. Freeman, p. 222, 1973.Wald, R. M. General Relativity. Chicago, IL: University of Chicago Press, p. 40, 1984.Weinberg, S. Gravitation and Cosmology: Principles and Applications of the General Theory of Relativity. New York: Wiley, p. 135, 1972.

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Scalar Curvature

Cite this as:

Weisstein, Eric W. "Scalar Curvature." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/ScalarCurvature.html

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