Noether Current of the Surface Term of Einstein-Hilbert Action, Virasoro Algebra, and Entropy

2012/10/27 by Bibhas Ranjan Majhi · 1 citation
Mathematics · Physics and Astronomy · #Algebra over a field #Algebra representation #Black Holes and Theoretical Physics #Black hole thermodynamics #Cellular algebra #Cosmology and Gravitation Theories #Entropy (arrow of time) #Invariant (physics) #Lagrangian #Mathematical physics #Mathematics #Noether's theorem #Noncommutative and Quantum Gravity Theories #Physics #Pure mathematics #Quantum mechanics #Term (time) #Virasoro algebra #gr-qc #hep-th

paper · pdf · doi:10.1155/2013/386342

published as Advances in High Energy Physics 2013 (2013) 386342 · V2: 18 pages, no figures, clarifications and references added

arxiv created 2012/10/27 · openalex publication_date 2013/01/01 · arxiv updated 2013/07/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

A derivation of Noether current from the surface term of Einstein-Hilbert action is given. We show that the corresponding charge, calculated on the horizon, is related to the Bekenstein-Hawking entropy. Also using the charge, the same entropy is found based on the Virasoro algebra and Cardy formula approach. In this approach, the relevant diffeomorphisms are found by imposing a very simple physical argument: diffeomorphisms keep the horizon structure invariant . This complements similar earlier results (Majhi and Padmanabhan (2012)) (arXiv:1204.1422) obtained from York-Gibbons-Hawking surface term. Finally we discuss the technical simplicities and improvements over the earlier attempts and also various important physical implications.

Citations

• Noether current from the surface term of gravitational action, Virasoro algebra and horizon entropy
• Entropy and temperature from black-hole/near-horizon-CFT duality
• Black Hole Thermodynamics from Euclidean Horizon Constraints
• A General Definition of "Conserved Quantities" in General Relativity and Other Theories of Gravity
• Conformal entropy as a consequence of the properties of stationary Killing horizons
• What we don't know about BTZ black hole entropy
• Statistical entropy of Schwarzschild black strings and black holes
• Near-Horizon Conformal Symmetry and Black Hole Entropy
• Black hole explosions?
• Path integral derivation of the Brown-Henneaux central charge
• Conformal field theory, (2 + 1)-dimensional gravity and the BTZ black hole
• Black Hole Entropy from Conformal Field Theory in Any Dimension
• Black hole entropy from classical Liouville theory
• Central charges in the canonical realization of asymptotic symmetries: An example from three dimensional gravity
• Some properties of the Noether charge and a proposal for dynamical black hole entropy
• Entropy from conformal field theory at Killing horizons
• Dynamics of diffeomorphism degrees of freedom at a horizon
• Black Holes and Entropy
• Symmetries, horizons, and black hole entropy

Cited by

• Noncommutative Heisenberg algebra in the neighbourhood of a generic null surface