Bach tensor

Bach tensor

In differential geometry and general relativity, the Bach tensor is a tensor of rank 2 which is conformally invariant. In abstract indices the Bach tensor is given by:B_{ab} = P_{cd}{C_a}^c}_b}^d+ abla^c abla_aP_{bc}- abla^c abla_cP_{ab}where "C" is the Weyl tensor, and "P" the Schouten tensor given in terms of the Ricci tensor "Ric" and scalar curvature "Sc" by

:P_{ab}=frac{1}{n-2}left(mathrm{Ric}_{ab}-frac{mathrm{Sc{2(n-1)}g_{ab} ight).


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