Boundary terms, variational principles, and higher derivative modified gravity

Journal Article · Thu Jan 15 00:00:00 EST 2009 · Physical Review. D, Particles Fields

DOI:https://doi.org/10.1103/PHYSREVD.79.024028· OSTI ID:21259823

Dyer, Ethan; Hinterbichler, Kurt ^[1]

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1. Institute for Strings, Cosmology and Astroparticle Physics and Department of Physics, Columbia University, New York, New York 10027 (United States)

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 through 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 Arnowitt-Deser-Misner energy in the Hamiltonian formalism, and the correct entropy for black holes in the semiclassical approximation.

• OSTI ID: 21259823
• Journal Information: Physical Review. D, Particles Fields, Vol. 79, Issue 2; Other Information: DOI: 10.1103/PhysRevD.79.024028; (c) 2009 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA); ISSN 0556-2821
• Country of Publication: United States
• Language: English

Related Subjects

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
BLACK HOLES
ENTROPY
GRAVITATION
HAMILTONIANS
SEMICLASSICAL APPROXIMATION
VARIATIONAL METHODS
VARIATIONS