Boundary Terms, Variational Principles and Higher Derivative Modified Gravity

Details Boundary Terms, Variational Principles and Higher Derivative Modified Gravity Boundary Terms, Variational Principles and Higher Derivative Modified Gravity

2008-09-23

arxiv.org/abs/0809.4033v2

Phys.Rev.D79:024028,2009

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

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

Scientific paper

10.1103/PhysRevD.79.024028

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.

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