## Abstract

A finite action principle for Einstein-Gauss-Bonnet anti-de Sitter gravity is achieved by supplementing the bulk Lagrangian by a suitable boundary term, whose form substantially differs in odd and even dimensions. For even dimensions, this term is given by the boundary contribution in the Euler theorem with a coupling constant fixed, demanding the spacetime to have constant (negative) curvature in the asymptotic region. For odd dimensions, the action is stationary under a boundary condition on the variation of the extrinsic curvature. A well-posed variational principle leads to an appropriate definition of energy and other conserved quantities using the Noether theorem, and to a correct description of black hole thermodynamics. In particular, this procedure assigns a nonzero energy to anti-de Sitter spacetime in all odd dimensions.

Original language | English |
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Article number | 084035 |

Journal | Physical Review D - Particles, Fields, Gravitation and Cosmology |

Volume | 74 |

Issue number | 8 |

DOIs | |

Publication status | Published - 2006 |

## ASJC Scopus subject areas

- Nuclear and High Energy Physics
- Physics and Astronomy (miscellaneous)