Variational principle and boundary terms in gravity à la Palatini

Abstract

A general $f(\mathcal{R})$ gravitational theory is considered within the Palatini formalism. By applying the variational principle and the usual conditions on the boundary, we show explicitly that a surface term remains such that as in their metric-compatible counterparts, an additional surface term has to be added in the gravitational action, which plays a fundamental role when calculating the entropy of the black hole.

arXiv comment5 pages, version to be published in PLB

References in corpus (10)

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• Born-Infeld inspired modifications of gravity
• Black Holes in f(R) theories
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• A Boundary Term for the Gravitational Action with Null Boundaries
• Thermodynamics in $f(R)$ gravity in the Palatini formalism
• Boundary Term in Metric f(R) Gravity: Field Equations in the Metric Formalism
• Finite Action in d5 Gauged Supergravity and Dilatonic Conformal Anomaly for Dual Quantum Field Theory
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Cited by in corpus (14)

• Scale-Invariant Quadratic Gravity and Inflation in the Palatini Formalism
• Tachyonic Preheating in Palatini $R^2$ Inflation
• Palatini $R^2$ Quintessential Inflation
• Implications of Palatini gravity for inflation and beyond
• Sudden singularities in generalized hybrid metric-Palatini cosmologies
• Cosmic strings in generalized hybrid metric-Palatini gravity
• 3+1 decomposition in modified gravities within the Palatini formalism and some applications
• On the well-posed variational principle in degenerate point particle systems using embeddings of the symplectic manifold
• Boundary Conditions for Constraint Systems in Variational Principle
• Determinantal Born-Infeld Coupling of Gravity and Electromagnetism
• Gravitational duality, Palatini variation and boundary terms: A synopsis
• $\beta$-function reconstruction of Palatini inflationary attractors
• Scalar-Induced Gravitational Waves in Palatini $f(R)$ Gravity
• Propagation and emission of gravitational waves in the weak-field limit within the Palatini formalism