High frequency quasi-normal modes for black holes with generic singularities: II. Asymptotically non-flat spacetimes

The possibility that the asymptotic quasi-normal mode (QNM) frequencies can be used to obtain the Bekenstein–Hawking entropy for the Schwarzschild black hole—commonly referred to as Hod's conjecture—has received considerable attention. To test this conjecture, using the monodromy technique, attempts have been made to analytically compute the asymptotic frequencies for a large class of black hole spacetimes. In an earlier work, two of the current authors computed the high frequency QNMs for scalar perturbations of ( D + 2)-dimensional spherically symmetric, asymptotically flat, single horizon spacetimes with generic power-law singularities. In this work, we extend these results to asymptotically non-flat spacetimes. Unlike in the earlier analyses, we treat asymptotically flat and de Sitter spacetimes in a unified manner, while the asymptotic anti-de Sitter spacetimes are considered separately. We obtain master equations for the asymptotic QNM frequency for all three cases. We show that for all three cases, the real part of the asymptotic QNM frequency—in general—is not proportional to ln(3), thus indicating that Hod's conjecture may be restrictive.