Abstract
We examine the black hole bomb model which consists of a rotating black hole of five-dimenensional minimal ungauged supergravity and a reflecting mirror around it. For low-frequency scalar perturbations, we find solutions to the Klein-Gordon equation in the near-horizon and far regions of the black hole spacetime. To avoid solutions with logarithmic terms, we assume that the orbital quantum number l takes on nearly, but not exactly, integervalues and perform the matching of these solutions in an intermediate region. This allows us to calculate analytically the frequency spectrum of quasinormal modes, taking the limits as l approaches even or odd integers separately. We find that all l modes of scalar perturbations undergo negative damping in the regime of superradiance, resulting in exponential growth of their amplitudes. Thus, the model under consideration would exhibit the superradiant instability, eventually behaving as a black hole bomb in five dimensions.
Highlights
The phenomenon of superradiance through which waves of certain frequencies are amplified when interacting with a medium has long been known in both classical and quantum non-gravitational systems
The analytical approach is based on a matching procedure, first introduced by Starobinsky [10], that allows one to find the complete lowfrequency solution to the Klein-Gordon equation by matching the near-horizon and far regions solutions in their overlap region
In our earlier work [25], using a similar analytical approach we gave a quantitative description of the superradiant instability of small rotating charged anti-de Sitter (AdS) black holes in five dimensions
Summary
The phenomenon of superradiance through which waves of certain frequencies are amplified when interacting with a medium has long been known in both classical and quantum non-gravitational systems. Developments in this direction have revealed that rotating black holes are stable to massless scalar, electromagnetic and gravitational perturbations [12, 13] On the contrary, it appeared that small perturbations of a massive scalar field grow exponentially in the superradiant regime, creating the instability of the system, the black hole bomb effect [17,18,19]. It is clear that the runaway behavior of such modes between the potential well and the horizon would result in their continuous reamplification, thereby causing the instability Another realization of the black hole bomb effect occurs in anti-de Sitter (AdS) spacetimes. For the superradiant modes to be excited there exists a critical radius and below this radius the system is stable These results allow one to clarify the instability of small Kerr-AdS black holes, as discussed in [24]. VI we end up with a discussion of our results
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