2006/09/30 by Jun-ichirou Koga
Physics and Astronomy · #Anomaly (physics) #Astrophysical Phenomena and Observations #Black Holes and Theoretical Physics #Black hole (networking) #Central charge #Conformal map #Cosmology and Gravitation Theories #Diffeomorphism #Geometry #Homogeneous space #Horizon #Killing vector field #Mathematical analysis #Mathematical physics #Physics #Quantum mechanics #Rotating black hole #Theoretical physics #gr-qc #hep-th
paper · pdf · doi:10.1088/0264-9381/25/4/045009
published as Class.Quant.Grav.25:045009,2008 · 14 pages, v2: references added, minor corrections, v3: new pars and refs. added and corresponding corrections
arxiv created 2007/03/12 · openalex publication_date 2008/02/05 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/08
We analyze asymptotic symmetries on the Killing horizon of the four-dimensional Kerr–Newman black hole. We first derive the asymptotic Killing vectors on the Killing horizon, which describe the asymptotic symmetries, and find that the general form of these asymptotic Killing vectors is the universal one possessed by arbitrary Killing horizons. We then construct the phase space associated with the asymptotic symmetries. It is shown that the phase space of an extreme black hole either has the size comparable with a non-extreme black hole, or is small enough to exclude degeneracy, depending on whether or not the global structure of a Killing horizon particular to an extreme black hole is respected. We also show that the classical central charge in the Poisson brackets algebra of these asymptotic symmetries vanishes, which implies that there is not an anomaly of diffeomorphism invariance. By taking into account other results in the literature, we argue that the vanishing central charge on a black hole horizon, in an effective theory, looks consistent with the thermal feature of a black hole. We furthermore argue that the vanishing central charge implies that there are sufficiently many classical configurations that constitute a single macroscopic state, while these configurations are distinguished physically.