Various Hamiltonian formulations of f(R) gravity and their canonical relationships

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

DOI:https://doi.org/10.1103/PHYSREVD.80.084032· OSTI ID:21325376

Deruelle, Nathalie; Youssef, Ahmed ^[1]; Sendouda, Yuuiti ^[2]

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1. APC, UMR 7164 du CNRS, Universite Paris 7, 75205 Paris (France)
2. Yukawa Institute for Theoretical Physics, Kyoto University, Kyoto 606-8502 (Japan)

Various Hamiltonian formulations of f(R) gravity can be found in the literature. Some authors follow the Ostrogradsky treatment of higher derivative theories and introduce as extra variables first order time derivatives of the metric (typically the extrinsic curvature). Some others take advantage of the conformal equivalence of f(R) theory with Einstein's gravity coupled to a scalar field and introduce as an extra variable the scalar curvature R itself, which includes second time derivatives of the metric. We show that, contrarily to some claims, these formulations are related by canonical transformations.

• OSTI ID: 21325376
• 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

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
CANONICAL TRANSFORMATIONS
GENERAL RELATIVITY THEORY
GRAVITATION
HAMILTONIANS
METRICS
SCALAR FIELDS