New Cases of Universality Theorem for Gravitational Theories
arXiv:1003.1617 · doi:10.1088/0264-9381/27/16/165021
Abstract
The "Universality Theorem" for gravity shows that f(R) theories (in their metric-affine formulation) in vacuum are dynamically equivalent to vacuum Einstein equations with suitable cosmological constants. This holds true for a generic (i.e. except sporadic degenerate cases) analytic function f(R) and standard gravity without cosmological constant is reproduced if f is the identity function (i.e. f(R)=R). The theorem is here extended introducing in dimension 4 a 1-parameter family of invariants R' inspired by the Barbero-Immirzi formulation of GR (which in the Euclidean sector includes also selfdual formulation). It will be proven that f(R') theories so defined are dynamically equivalent to the corresponding metric-affine f(R) theory. In particular for the function f(R)=R the standard equivalence between GR and Holst Lagrangian is obtained.
10 pages, few typos corrected
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Cited by in corpus (8)
- Hamiltonian Formulation of Palatini f(R) theories a la Brans-Dicke
- Palatini Actions and Quantum Gravity Phenomenology
- The physical foundations for the geometric structure of relativistic theories of gravitation. From General Relativity to Extended Theories of Gravity through Ehlers-Pirani-Schild approach
- New Cases of Universality Theorem for Gravitational Theories
- Extended Loop Quantum Gravity
- Generalized Chern-Simons Modified Gravity in First-Order Formalism
- Inducing Barbero-Immirzi Connections along SU(2)-reductions of Bundles on Spacetime
- Barbero-Immirzi connections and how to build them