Boundary Terms, Variational Principles and Higher Derivative Modified Gravity

By Ethan Dyer, Kurt Hinterbichler. 2008

196 citations recorded by the source corpus.

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.

Subfields: Astronomy and Astrophysics, Nuclear and High Energy Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/6d146fa27ae30da5ed7d6ea5537ebb5a54eee332

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Citations in the corpus

Symmetries for Galileons and DBI scalars on curved space (2011, background): “Similarly, Lovelock gravity in the bulk must be supplemented by brane terms which depend on the intrinsic and extrinsic curvature of the brane (the so-called Myers terms [43, 44]), which are needed in order to make the variational problem for the brane/bulk system well posed [45].”
Theoretical Aspects of Massive Gravity (2011, methodology): “To have a well defined variational principle, we must have Gibbons-Hawking terms on both sides [100], corresponding to the outward pointing normals.”
f(R) Theories (2010, background): “In doing so one requires a surface term [222, 482, 69, 48, 49, 286], which is known as the Hawking–Luttrell term [295] (analogous to the York–Gibbons– Hawking one for General Relativity).”
Beyond the Cosmological Standard Model (2014, unknown): “In [392], the variational principle of higher-derivative theories is examined and formulated systematically.”