Poisson Algebra of Diffeomorphism Generators in a Spacetime Containing a Bifurcation

Abstract

In this article we will analyze the possibility of a nontrivial central extension of the Poisson algebra of the diffeomorphism generators, which respect certain boundary conditions on the black hole bifurcation. The origin of a possible central extension in the algebra is due to the existence of boundary terms in the in the canonical generators. The existence of such boundary terms depend on the exact boundary conditions one takes. We will check two possible boundary conditions i.e. fixed bolt metric and fixed surface gravity. In the case of fixed metric the the action acquires a boundary term associated to the bifurcation but this is canceled in the Legendre transformation and so absent in the canonical generator and so in this case the possibility of a nontrivial central extension is ruled out. In the case of fixed surface gravity the boundary term in the action is absent but present in the Hamiltonian. Also in this case we will see that there is no nontrivial central extension, also if there exist a boundary term in the generator.

LaTex 20 pages, some misprints corrected, 2 references added. Accepted for publication on Phys. Rev. D

References in corpus (35)

• The Black Hole in Three Dimensional Space Time
• Microscopic Origin of the Bekenstein-Hawking Entropy
• Black Hole Entropy is Noether Charge
• Some Properties of Noether Charge and a Proposal for Dynamical Black Hole Entropy
• The dS/CFT Correspondence
• Black Hole Entropy from Near-Horizon Microstates
• Quantum Geometry and Black Hole Entropy
• Black Hole Entropy from Conformal Field Theory in Any Dimension
• A comparison of Noether charge and Euclidean methods for Computing the Entropy of Stationary Black Holes
• The asymptotic dynamics of three-dimensional Einstein gravity with a negative cosmological constant
• Entropy from Conformal Field Theory at Killing Horizons
• Conformal description of horizon's states
• Asymptotic symmetries of AdS_2 and conformal group in d=1
• Statistical Entropy of Three-dimensional Kerr-De Sitter Space
• Mechanism of Generation of Black Hole Entropy in Sakharov's Induced Gravity
• Some Aspects of the de Sitter/CFT Correspondence
• The Hamiltonian Dynamics of Bounded Spacetime and Black Hole Entropy: The Canonical Method
• The Gravitational Hamiltonian in the Presence of Non-Orthogonal Boundaries
• Asymptotic symmetries on Killing horizons
• Black hole entropy and thermodynamics from symmetries
• Symmetry Algebras in Chern-Simons Theories with Boundary: Canonical Approach
• Diffeomorphism on Horizon as an Asymptotic Isometry of Schwarzschild Black Hole
• Black hole entropy calculations based on symmetries
• Comments on `` Black Hole Entropy from Conformal Field Theory in Any Dimension ''
• The Asymptotic Dynamics of de Sitter Gravity in three Dimensions
• De Sitter Gravity and Liouville Theory
• Black hole entropy from classical Liouville theory
• Quantum Liouville theory and BTZ black hole entropy
• Two-dimensional black holes as open strings: A new realization of the ADS/CFT correspondence
• Causal Boundary Entropy From Horizon Conformal Field Theory
• Black hole entropy from Poisson brackets (demystification of some calculations)
• Central charges and boundary fields for two dimensional dilatonic black holes
• Higher curvature Lagrangians, conformal symmetry and microscopic entropy of Killing horizons
• Classical Liouville Theory and the Microscopic Interpretation of Black Hole Entropy
• Two Dimensional Conformal Symmetry and the Microscopic Interpretation of Black Hole Entropy

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• Lanczos-Lovelock models of gravity
• Noether Current, Horizon Virasoro Algebra and Entropy
• Noether current of the surface term of Einstein-Hilbert action, Virasoro algebra and entropy
• Gravitational anomalies and entropy
• No-core shell model for A = 47 and A = 49
• Description of Black Hole Microstates by Means of a Free Affine-Scalar Field