ar X iv : g r - qc / 0 10 51 08 v 1 2 8 M ay 2 00 1 Non - trivial Solutions of the Bach Equation Exist
نویسنده
چکیده
We show that solutions of the Bach equation exist which are not conformal Einstein spaces. In connection with fourth order gravitational field equations, cf. e.g. [1, 2] where the breaking of conformal invariance was discussed, the original Bach equation, Bij = 0 , (1) enjoys current interest. Eq. (1) stems from a Lagrangian L = 1 2 √ −gCijklC , and variation gives, cf. Bach [3], 1 √−g δL/δg ij = Bij = 2C a b ij ;ba + C a b ij Rba . An Einstein space, Rij = λgij , (2)
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