Trace-free Ricci tensor

Encyclopedia : T : TR : TRA : Trace-free Ricci tensor

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

[\tilde_ \, =R_- \fracg_]

where [\, R_] is the Ricci tensor, [\, R] the Ricci scalar (=[\, R^a_a]) and [\, g_] is the metric tensor.

It is so called as it's trace vanishes:

[\tilde^a_a=\, 0]

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

See also