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The contraction of the Riemann curvature tensor entering the Einstein field equation.
Index and sign conventions depend on the convention for the Riemann tensor.
wp-ricci_tensornlab-ricci_tensortong-grEach relation below ends at this concept.
This is an authored directed relation from the source endpoint to the target endpoint.
Contracting the Riemann tensor gives the Ricci tensor.
Apply a standard functorial or canonical construction whose output is not merely a reduct of the input and is not generally an equivalent presentation of the same object.
wp-riemann_curvature_tensornlab-riemann_curvature_tensortong-grwp-ricci_tensornlab-ricci_tensorEach relation below starts at this concept.
This is an authored directed relation from the source endpoint to the target endpoint.
Combining Ricci and scalar curvature gives the Einstein tensor.
Apply a standard functorial or canonical construction whose output is not merely a reduct of the input and is not generally an equivalent presentation of the same object.
wp-ricci_tensornlab-ricci_tensortong-grwp-einstein_tensornlab-einstein_tensoreinstein-equationThis is an authored directed relation from the source endpoint to the target endpoint.
Tracing Ricci curvature with the inverse metric gives scalar curvature.
Apply a standard functorial or canonical construction whose output is not merely a reduct of the input and is not generally an equivalent presentation of the same object.
wp-ricci_tensornlab-ricci_tensortong-grwp-scalar_curvaturenlab-scalar_curvature