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.
Highlights
The beautiful phenomenon of superradiance found a generic realisation in black hole (BH) physics: the ability of extracting energy and angular momentum from rotating BHs — see Ref. [1] for a recent review and Ref. [2] for a mathematically rigorous treatment
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 results allow us to conclude that, for a given BTZ BH and massive scalar field, there exists a range of Robin boundary conditions (RBCs) for which there are mode solutions whose energy flux across the horizon is negative, that is, the energy flux is towards the exterior region of the BH
Summary
The beautiful phenomenon of superradiance found a generic realisation in black hole (BH) physics: the ability of extracting energy and angular momentum from rotating BHs — see Ref. [1] for a recent review and Ref. [2] for a mathematically rigorous treatment. The beautiful phenomenon of superradiance found a generic realisation in black hole (BH) physics: the ability of extracting energy and angular momentum from rotating BHs — see Ref. [2] for a mathematically rigorous treatment This extraction is mediated by low frequency Bosonic modes, which get amplified upon scattering off the rotating BH and grow exponentially, becoming an instability if trapped in the vicinity of the BH. Quite recently, interesting progress has been achieved towards understanding the end state of the superradiant instability of the Kerr BH [16,17], possible leading to an equilibrium state between the field and the (spun down) BH [18,19,20]. An intriguing exception to this rule is the geometrically elegant three-dimensional BTZ BH [26,27], which does not exhibit superradiance, for the simplest Bosonic field model and simplest (field vanishing, i.e., Dirichlet) boundary conditions of the Bosonic field at infinity [28]
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