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A capital R with two indices, a contraction of the Riemann tensor.
Also known as: Ricci tensor, Ricci curvature, R mu nu
The Ricci tensor is what you get by summing the Riemann tensor over two of its indices, and it is the part of curvature that matter directly produces. Vacuum solutions of Einstein's equations set it to zero — which does not mean the space is flat, only that no matter is present.
Denotes the Ricci tensor, the trace of the Riemann tensor over its first and third indices.
Contexts: Laboratory
Appears directly in the Einstein field equations, where it is sourced by the energy and momentum present.
Contexts: Laboratory
Is zero in vacuum without the space being flat, which is why gravitational waves and black holes exist outside matter.
Contexts: Laboratory
An italic capital letter R carrying two small Greek index letters set below and to the right.