2011/06/30 by Stefano Bertini, Sergio L. Cacciatori, Dietmar Klemm · 3 citations
Mathematics · Physics and Astronomy · #Astrophysical Phenomena and Observations #Black Holes and Theoretical Physics #Black hole (networking) #Conformal map #Conformal symmetry #Cosmology and Gravitation Theories #General relativity #Geometry #Kerr metric #Mathematical physics #Mathematics #Physics #Quantum mechanics #Scalar (mathematics) #Schwarzschild geodesics #Schwarzschild metric #Schwarzschild radius #Spacetime #gr-qc #hep-th
paper · pdf · doi:10.1103/physrevd.85.064018
17 pages, uses JHEP3.cls. v2: Minor correction in appendix. v3: Final version to appear in PRD
arxiv created 2012/02/25 · openalex publication_date 2012/03/16 · arxiv updated 2013/05/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We show that the scalar wave equation at low frequencies in the Schwarzschild geometry enjoys a hidden SL(2,ℝ) invariance, which is not inherited from an underlying symmetry of the spacetime itself. Contrary to what happens for Kerr black holes, the vector fields generating the SL(2,ℝ) are globally defined. Furthermore, it turns out that under an SU(2, 1) Kinnersley transformation, which maps the Schwarzschild solution into the near-horizon limit AdS2\ifmmode×\else\texttimes\fiS2 of the extremal Reissner-Nordstr"om black hole (with the same entropy), the Schwarzschild hidden symmetry generators become exactly the isometries of the AdS2 factor. Finally, we use the SL(2,ℝ) symmetry to determine algebraically the quasinormal frequencies of the Schwarzschild black hole and show that this yields the correct leading behavior for large damping.