Palatini Variational Principle for an Extended Einstein-Hilbert Action
arXiv:gr-qc/9711003 · doi:10.1103/PhysRevD.57.4754
Abstract
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.
14 pages, LaTeX
References in corpus (1)
Cited by in corpus (14)
- f(R) Theories Of Gravity
- Palatini Approach to Modified Gravity: f(R) Theories and Beyond
- How (Not) to Palatini
- Higgs inflation in the Palatini formulation with kinetic terms for the metric
- Family of scalar-nonmetricity theories of gravity
- A correspondence between modified gravity and General Relativity with scalar fields
- General Relativity with Local Space-time Defects
- Projective and amplified symmetries in metric-affine theories
- Extended Palatini action for general relativity and the natural emergence of the cosmological constant
- Compact scalar field solutions in EiBI gravity
- Weyl frames and canonical transformations in geometrical scalar-tensor theories of gravity
- Homogeneous Cosmological Models in Weyl's Geometrical Scalar-Tensor Theory
- A Generalization of Gravity
- Diffeomorphism-invariant Covariant Hamiltonians of a pseudo-Riemannian Metric and a Linear Connection