Trace-free Ricci tensor

From Freepedia

In mathematics and general relativity, the trace-free Ricci tensor is the tensor defined by

<math>\tilde{R}_{ab} \, =R_{ab}- \frac{R}{4}g_{ab}</math>

where <math>\, R_{ab}</math> is the Ricci tensor, <math>\, R</math> the Ricci scalar (=<math>\, R^a{}_a</math>) and <math>\, g_{ab}</math> is the metric tensor.

It is so called as it's trace vanishes:

<math>\tilde{R}^a{}_a=\, 0</math>

The trace-free Ricci tensor is useful in the study of exact solutions of Einstein's field equations of general relativity.