Phys. Rev. D 57, 4754–4759 (1998)Palatini variational principle for an extended Einstein-Hilbert actionReceived 10 November 1997; published in the issue dated 15 April 1998 We consider a Palatini variation on a generalized Einstein-Hilbert action. We find that the Hilbert constraint—that the connection equals the Christoffel symbol—arises only as a special case of this general action, while, for particular values of the coefficients of this generalized action, the connection is completely unconstrained. We discuss the relationship between this situation and that usually encountered in the Palatini formulation. © 1998 The American Physical Society URL:
http://link.aps.org/doi/10.1103/PhysRevD.57.4754
DOI:
10.1103/PhysRevD.57.4754
PACS:
04.20.Fy
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