The Fefferman-Graham Ambiguity and AdS Black Holes

Abstract

Asymptotically anti-de Sitter space-times in pure gravity with negative cosmological constant are described, in all space-time dimensions greater than two, by classical degrees of freedom on the conformal boundary at space-like infinity. Their effective boundary action has a conformal anomaly for even dimensions and is conformally invariant for odd ones. These degrees of freedom are encoded in traceless tensor fields in the Fefferman-Graham asymptotic metric for any choice of conformally flat boundary and generate all Schwarzschild and Kerr black holes in anti-de Sitter space-time. We argue that these fields describe components of an energy-momentum tensor of a boundary theory and show explicitly how this is realized in 2+1 dimensions. There, the Fefferman-Graham fields reduce to the generators of the Virasoro algebra and give the mass and the angular momentum of the BTZ black holes. Their local expression is the Liouville field in a general curved background.

Latex, 14 pages; one reference modified, minor misprints corrected

References in corpus (5)

• Quantum effective action from the AdS/CFT correspondence
• Volume and Area Renormalizations for Conformally Compact Einstein Metrics
• Super Weyl Anomalies in the AdS/CFT Correspondence
• Counterterms for the Dirichlet Prescription of the AdS/CFT Correspondence
• Diffeomorphisms and Weyl transformations in AdS_3 gravity

Cited by in corpus (22)

• Aspects of the BMS/CFT correspondence
• Setting the boundary free in AdS/CFT
• Conformal Field Theory, (2+1)-Dimensional Gravity, and the BTZ Black Hole
• Quantum Gravity in 2+1 Dimensions: The Case of a Closed Universe
• Gravity in Warped Compactifications and the Holographic Stress Tensor
• Enhanced asymptotic symmetry algebra of AdS3
• Dynamics of Asymptotic Diffeomorphisms in (2+1)-Dimensional Gravity
• 3D Gravity, Point Particles and Liouville Theory
• Holonomies, anomalies and the Fefferman-Graham ambiguity in AdS3 gravity
• Ambient metrics for $n$-dimensional $pp$-waves
• Uniqueness of the asymptotic AdS3 geometry
• Non-Quasinormal Modes and Black Hole Physics
• Obstruction Tensors in Weyl Geometry and Holographic Weyl Anomaly
• On the Boundary Dynamics of Chern-Simons Gravity
• Liouville Lost, Liouville Regained: Central Charge in a Dynamical Background
• Holography and the Polyakov action
• The gravitational dynamics of kinematic space
• Symmetries and Charges in Weyl-Fefferman-Graham Gauge
• Conformal Gravity from AdS/CFT mechanism
• Thermodynamics of nonspherical black holes from Liouville theory
• Poisson Structure of the Boundary Gravitons in 3D Gravity with Negative $\Lambda$
• The Near-Boundary Geometry of Einstein-Vacuum Asymptotically Anti-de Sitter Spacetimes