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Trace-free Ricci tensor

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

\tilde{R}_{ab}=R_{ab}- \frac{R}{4}g_{ab}

where Rab is the Ricci tensor, R is the Ricci scalar (=Raa) and gab is the metric tensor.

It is so called as it's trace vanishes:

\tilde{R}^a{}_a=0

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

Last updated: 06-05-2005 01:39:30
Science Fair Project Encyclopedia Contents Page
10-26-2009 08:16:03
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