Superradiance in the BTZ black hole with Robin boundary conditions

Abstract

We show the existence of superradiant modes of massive scalar fields propagating in BTZ black holes when certain Robin boundary conditions, which never include the commonly considered Dirichlet boundary conditions, are imposed at spatial infinity. These superradiant modes are defined as those solutions whose energy flux across the horizon is towards the exterior region. Differently from rotating, asymptotically flat black holes, we obtain that not all modes which grow up exponentially in time are superradiant; for some of these, the growth is sourced by a bulk instability of AdS3, triggered by the scalar field with Robin boundary conditions, rather than by energy extraction from the BTZ black hole. Thus, this setup provides an example wherein Bosonic modes with low frequency are pumping energy into, rather than extracting energy from, a rotating black hole.1 See also [33] for a discussion of the quantum field theory of a massive scalar field in the BTZ BH with RBCs.

Quantum-corrected rotating black holes and naked singularities in ( 2+1 ) dimensions

“…For superradiance, see [40,41] in Kerr and [42] in asymptotically-AdS Kerr. In BTZ, on the other hand, a massless scalar field obeying Dirichlet boundary conditions does not exhibit superradiance [43], although the specific case of a massive scalar field obeying certain Robin boundary conditions does exhibit superradiance [44].…”

Superradiant instabilities in the Kerr-mirror and Kerr-AdS black holes with Robin boundary conditions

“…However, it was also observed in Ref. [1] that not all of the modes which grow exponentially in time extract energy from the BH. This behavior was interpreted as due to an intrinsic, bulk instability of the AdS space, which occurs for certain RBCs, as previously noted in Ref.…”

“…However, the same is guaranteed by Robin boundary conditions (RBCs), a more generic choice which has not yet been thoroughly studied in the literature. Exceptions include some recent studies within the (2 þ 1)-dimensional Bañados-Teitelboim-Zanelli (BTZ) BH [1,28] and some studies for spin-1 fields [29,30].…”

“…The study of a massive scalar field with RBCs in a rotating BTZ BH [1] showed that, unlike for DBCs, a superradiant instability can occur, the signatures of which are some exponentially growing modes that extract energy from the BH. However, it was also observed in Ref.…”

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It has been recently observed that a scalar field with Robin boundary conditions (RBCs) can trigger both a superradiant and a bulk instability for a Bañados-Teitelboim-Zanelli (BTZ) black hole (BH) [1]. To understand the generality and scrutinize the origin of this behavior, we consider here the superradiant instability of a Kerr BH confined either in a mirrorlike cavity or in anti-de Sitter (AdS) space, triggered also by a scalar field with RBCs.

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