2003/01/31 by Alex Giacomini, A. Giacomini, Nicola Pinamonti +1 · 5 citations
Mathematics · Physics and Astronomy · #Algebra over a field #Algebra representation #Ansatz #Black Holes and Theoretical Physics #Black hole (networking) #Black hole thermodynamics #Central charge #Circular symmetry #Conformal field theory #Conformal map #Conformal symmetry #Cosmology and Gravitation Theories #Entropy (arrow of time) #Lie algebra #Lie conformal algebra #Liouville field theory #Mathematical analysis #Mathematical physics #Mathematics #Noncommutative and Quantum Gravity Theories #Physics #Pure mathematics #Quantum #Quantum gravity #Quantum mechanics #Rotating black hole #Virasoro algebra #Witt algebra #gr-qc #hep-th
paper · pdf · doi:10.1088/1126-6708/2003/02/014
published as JHEP 0302 (2003) 014 · LaTeX, 11 pages, to appear on JHEP
openalex publication_date 2003/02/07 · arxiv created 2003/02/10 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
In this article we compute the black hole entropy by finding a classical central charge of the Virasoro algebra of a Liouville theory using the Cardy formula. This is done by performing a dimensional reduction of the Einstein Hilbert action with the ansatz of spherical symmetry and writing the metric in conformally flat form. We obtain two coupled field equations. Using the near horizon approximation the field equation for the conformal factor decouples. The one concerning the conformal factor is a Liouville equation, it posses the symmetry induced by a Virasoro algebra. We argue that it describes the microstates of the black hole, namely the generators of this symmetry do not change the thermodynamical properties of the black hole.