Boundary Terms, Variational Principles and Higher Derivative Modified Gravity

Abstract

We discuss the criteria that must be satisfied by a well-posed variational principle. We clarify the role of Gibbons-Hawking-York type boundary terms in the actions of higher derivative models of gravity, such as F(R) gravity, and argue that the correct boundary terms are the naive ones obtained though the correspondence with scalar-tensor theory, despite the fact that variations of normal derivatives of the metric must be fixed on the boundary. We show in the case of F(R) gravity that these boundary terms reproduce the correct ADM energy in the hamiltonian formalism, and the correct entropy for black holes in the semi-classical approximation.

54 pages, 2 figures. Several typos corrected, references added. Version appearing in PRD

References in corpus (7)

• f(R) Theories Of Gravity
• Models of f(R) Cosmic Acceleration that Evade Solar-System Tests
• Avoiding Dark Energy with 1/R Modifications of Gravity
• Limit to General Relativity in f(R) theories of gravity
• Quantum Gravity and Higher Curvature Actions
• Black hole entropy in modified gravity models
• The cosmological constant as an eigenvalue of f(R)-gravity Hamiltonian constraint

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