Einstein-Gauss-Bonnet theory of gravity: The Gauss-Bonnet-Katz boundary term

Abstract

We propose a boundary term to the Einstein-Gauss-Bonnet action for gravity, which is constructed as the dimensional continuation of the Chern-Weil theorem, and such that the extremization of the full action yields the equations of motion when Dirichlet boundary conditions are imposed. When translated into tensorial language, this boundary term is the generalization to this theory of the Katz boundary term and vector for general relativity. The construction allows to deal with a general background and includes the Gibbons-Hawking-Myers boundary term as a special case, when the background is taken to be a product manifold. As a first application we show that this Einstein Gauss-Bonnet Katz action yields, without any extra ingredients or regularization, the expected mass of the Boulware-Deser black hole.

arXiv comment13 pages

References in corpus (17)

• The Gravitational Hamiltonian, Action, Entropy, and Surface Terms
• Generalised Israel Junction Conditions for a Gauss-Bonnet Brane World
• Relativistic conservation laws and integral constraints for large cosmological perturbations
• Israel conditions for the Gauss-Bonnet theory and the Friedmann equation on the brane universe
• Regularization of odd-dimensional AdS gravity: Kounterterms
• Universal regularization prescription for Lovelock AdS gravity
• Conserved Charges in Einstein Gauss-Bonnet theory
• Transgression forms and extensions of Chern-Simons gauge theories
• Counterterms in Dimensionally Continued AdS Gravity
• On the quasi-linearity of the Einstein- "Gauss-Bonnet" gravity field equations
• On boundary conditions in three-dimensional AdS gravity
• General Relativity from a gauged WZW term
• A Novel Derivation of the Boundary Term for the Action in Lanczos-Lovelock Gravity
• On Global Conservation Laws at Null Infinity
• Mass and angular momenta of Kerr anti-de Sitter spacetimes in Einstein-Gauss-Bonnet theory
• Even-dimensional topological gravity from Chern-Simons gravity
• Chern-Weil theorem, Lovelock Lagrangians in critical dimensions and boundary terms in gravity actions

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