Black-hole bomb and superradiant instabilities

Abstract

A wave impinging on a Kerr black hole can be amplified as it scatters off the hole if certain conditions are satisfied giving rise to superradiant scattering. By placing a mirror around the black hole one can make the system unstable. This is the black hole bomb of Press and Teukolsky. We investigate in detail this process and compute the growing timescales and oscillation frequencies as a function of the mirror's location. It is found that in order for the system black hole plus mirror to become unstable there is a minimum distance at which the mirror must be located. We also give an explicit example showing that such a bomb can be built. In addition, our arguments enable us to justify why large Kerr-AdS black holes are stable and small Kerr-AdS black holes should be unstable.

Classical instability of Kerr-AdS black holes and the issue of final state

“…From a superradiance point of view, this is because the characteristic modes of large AdS holes are very large and do not satisfy the superradiant condition ω < mΩ H (see [20,21,23] for details). Here ω and m are the frequency and angular momentum of the mode, and Ω H is the horizon velocity of the black hole.…”

“…One might worry that any rotating black hole in AdS space might be unstable against superradiance: a rotating black hole amplifies some incoming waves, and since AdS is a box-like spacetime, the amplified radiation would be reflected back, and so on, leading to a black hole bomb [19,20,21], or exponential growth of any perturbation. Two major results were reported:…”

“…(ii) small (r + < ℓ) Kerr-AdS black holes are unstable against scalar perturbations [21], precisely by a black hole bomb mechanism. The value r + = r c + = √ aℓ, which obviously depends on the rotation parameter a, plays a critical role.…”

“…(i) large (r + > ℓ) Kerr-AdS are stable [20,21,22] (where r + is the horizon radius and ℓ is the cosmological length). From a superradiance point of view, this is because the characteristic modes of large AdS holes are very large and do not satisfy the superradiant condition ω < mΩ H (see [20,21,23] for details).…”

Black hole bombs and explosions: from astrophysics to particle physics

“…Indeed, it was first shown in Ref. [55] that small rotating anti-de Sitter black holes are unstable against a superradiant mechanism. This study was generalized to other geometries and perturbation sectors [56,57,58,59,60].…”