The mass of asymptotically anti-de Sitter space-times

Abstract

We give a definition of mass for spacelike hypersurfaces in space-times with metrics which are asymptotic to the anti-de Sitter one, or to a class of generalizations thereof. We present the results of gr-qc/0110014 which show that our definition provides a geometric invariant for a spacelike hypersurface embedded in a space-time. Some further global invariants are also given.

6 pages, revtex4 with several style files; Revised version, esentially identical to the one published in CQG, puts emphasis on the Hamiltonian character of our analysis, which implies uniqueness of the resulting energy expression. Reference list expanded, including reference to gr-qc/0110014 and math.DG/0110035, where proofs of the results presented here are given

References in corpus (8)

• A General Definition of "Conserved Quantities" in General Relativity and Other Theories of Gravity
• Asymptotically Anti-de Sitter Space-times: Conserved Quantities
• Stress Tensors and Casimir Energies in the AdS/CFT Correspondence
• Towards the classification of static vacuum spacetimes with negative cosmological constant
• Currents and Superpotentials in classical gauge theories: II. Global aspects and the example of Affine gravity
• New Five Dimensional Black Holes Classified by Horizon Geometry, and a Bianchi VI Braneworld
• Boundary conditions at spatial infinity from a Hamiltonian point of view
• The mass of asymptotically hyperbolic Riemannian manifolds

Cited by in corpus (15)

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• Spherically symmetric black holes in $f(R)$ gravity: Is geometric scalar hair supported ?
• Rigid upper bounds for the angular momentum and centre of mass of non-singular asymptotically anti-de Sitter space-times
• The cosmological constant and the energy of gravitational radiation
• On mapping properties of the general relativistic constraints operator in weighted function spaces, with applications
• The Trautman-Bondi mass of initial data sets
• Non-singular, vacuum, stationary space-times with a negative cosmological constant
• The hyperbolic positive energy theorem
• On the mass aspect function and positive energy theorems for asymptotically hyperbolic manifolds
• Hamiltonian dynamics in the space of asymptotically Kerr-de Sitter spacetimes
• Non-singular spacetimes with a negative cosmological constant: III. Stationary solutions with matter fields
• Einstein black holes, free scalars and AdS/CFT correspondence
• Quasi-local energy with respect to de Sitter/anti-de Sitter reference
• Small sphere limit of the quasi-local energy with anti de-Sitter space reference
• Relative radial mass and rigidity of some warped product manifolds