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.

5 pages, version to be published in PLB

References in corpus (2)

• Palatini Approach to Modified Gravity: f(R) Theories and Beyond
• Noether Charge and Black Hole Entropy in Modified Theories of Gravity

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• Determinantal Born-Infeld Coupling of Gravity and Electromagnetism
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• $\beta$-function reconstruction of Palatini inflationary attractors
• Scalar-Induced Gravitational Waves in Palatini $f(R)$ Gravity
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