Extended Palatini action for general relativity

Journal Article · Thu Oct 15 04:00:00 EDT 2009 · Physical Review. D, Particles Fields

DOI:https://doi.org/10.1103/PHYSREVD.80.084029· OSTI ID:21325373

Rosenthal, Eran ^[1]

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1. Center for Radiophysics and Space Research, Cornell University, Ithaca, New York 14853 (United States)

In the Palatini action of general relativity, the connection and the metric are treated as independent dynamical variables. Instead of assuming a relation between these quantities, the desired relation between them is derived through the Euler-Lagrange equations of the Palatini action. In this manuscript we construct an extended Palatini action, where we do not assume any a priori relationship between the connection, the covariant metric tensor, and the contravariant metric tensor. Instead we treat these three quantities as independent dynamical variables. We show that this action reproduces the standard Einstein field equations depending on a single metric tensor. We further show that in vacuum and in the absence of cosmological constant this theory has an enhanced symmetry.

• OSTI ID: 21325373
• Journal Information: Physical Review. D, Particles Fields, Journal Name: Physical Review. D, Particles Fields Journal Issue: 8 Vol. 80; ISSN PRVDAQ; ISSN 0556-2821
• Country of Publication: United States
• Language: English

Related Subjects

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
COSMOLOGICAL CONSTANT
EINSTEIN FIELD EQUATIONS
GENERAL RELATIVITY THEORY
LAGRANGE EQUATIONS
METRICS
SYMMETRY