Palatini versus metric formulation in higher-curvature gravity

Journal Article · Sat Nov 15 04:00:00 EST 2008 · Journal of Cosmology and Astroparticle Physics

DOI:https://doi.org/10.1088/1475-7516/2008/11/008· OSTI ID:22156813

Borunda, Monica; Janssen, Bert; Bastero-Gil, Mar ^[1]

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1. Departamento de Fisica Teorica y del Cosmos and Centro Andaluz de Fisica de Particulas Elementales, Universidad de Granada, E-18071 Granada (Spain)

We compare the metric and the Palatini formalism to obtain the Einstein equations in the presence of higher-order curvature corrections that consist of contractions of the Riemann tensor, but not of its derivatives. We find that there is a class of theories for which the two formalisms are equivalent. This class contains the Palatini version of Lovelock theory, but also more Lagrangians that are not Lovelock, but respect certain symmetries. For the general case, we find that imposing the Levi-Civita connection as an ansatz, the Palatini formalism is contained within the metric formalism, in the sense that any solution of the former also appears as a solution of the latter, but not necessarily the other way around. Finally we give the conditions the solutions of the metric equations should satisfy in order to solve the Palatini equations.

• OSTI ID: 22156813
• Journal Information: Journal of Cosmology and Astroparticle Physics, Journal Name: Journal of Cosmology and Astroparticle Physics Journal Issue: 11 Vol. 2008; ISSN 1475-7516
• Country of Publication: United States
• Language: English

Related Subjects

79 ASTRONOMY AND ASTROPHYSICS
CONTRACTION
EINSTEIN FIELD EQUATIONS
GRAVITATION
LAGRANGIAN FUNCTION
MATHEMATICAL SOLUTIONS
METRICS
RIEMANN SPACE
SYMMETRY
TENSORS