Conformal structure of a Schwarzschild black hole immersed in a Friedman universe (original) (raw)

We show that the scalar wave equation at low frequencies in the Schwarzschild geometry enjoys a hidden SLð2; RÞ 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 SLð2; RÞ 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 AdS 2 Â S 2 of the extremal Reissner-Nordström black hole (with the same entropy), the Schwarzschild hidden symmetry generators become exactly the isometries of the AdS 2 factor. Finally, we use the SLð2; RÞ symmetry to determine algebraically the quasinormal frequencies of the Schwarzschild black hole and show that this yields the correct leading behavior for large damping.