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Title: 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 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.

Authors:
;  [1]
  1. Institute for Strings, Cosmology and Astroparticle Physics and Department of Physics, Columbia University, New York, New York 10027 (United States)
Publication Date:
OSTI Identifier:
21259823
Resource Type:
Journal Article
Journal Name:
Physical Review. D, Particles Fields
Additional Journal Information:
Journal Volume: 79; Journal Issue: 2; Other Information: DOI: 10.1103/PhysRevD.79.024028; (c) 2009 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 0556-2821
Country of Publication:
United States
Language:
English
Subject:
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; BLACK HOLES; ENTROPY; GRAVITATION; HAMILTONIANS; SEMICLASSICAL APPROXIMATION; VARIATIONAL METHODS; VARIATIONS

Citation Formats

Dyer, Ethan, and Hinterbichler, Kurt. Boundary terms, variational principles, and higher derivative modified gravity. United States: N. p., 2009. Web. doi:10.1103/PHYSREVD.79.024028.
Dyer, Ethan, & Hinterbichler, Kurt. Boundary terms, variational principles, and higher derivative modified gravity. United States. https://doi.org/10.1103/PHYSREVD.79.024028
Dyer, Ethan, and Hinterbichler, Kurt. 2009. "Boundary terms, variational principles, and higher derivative modified gravity". United States. https://doi.org/10.1103/PHYSREVD.79.024028.
@article{osti_21259823,
title = {Boundary terms, variational principles, and higher derivative modified gravity},
author = {Dyer, Ethan and Hinterbichler, Kurt},
abstractNote = {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.},
doi = {10.1103/PHYSREVD.79.024028},
url = {https://www.osti.gov/biblio/21259823}, journal = {Physical Review. D, Particles Fields},
issn = {0556-2821},
number = 2,
volume = 79,
place = {United States},
year = {Thu Jan 15 00:00:00 EST 2009},
month = {Thu Jan 15 00:00:00 EST 2009}
}