Generalized superradiant scattering

Abstract

We analyse the necessary and sufficient conditions for the occurance of superradiance. Starting with a wave equation we examine the possibility of superradiance in terms of an effective potential and boundary conditions. In particular, we show that the existence of an ergoregion is not sufficient; an appropriate boundary condition, e.g. only ingoing group velocity waves at an event horizon, is also crucial. After applying our scheme to the standard examples of superradiance, we show that analogue models of gravity without an event horizon do not necessarily exhibit superradiance. Particularly, we show that the superradiant phenomenon is absent in purely rotating inviscid fluids with vorticity. We argue that there should be a catalogue of superradiant systems that can be found by focusing on the necessary and sufficient conditions outlined below.PACS numbers: 98.80. Qc,47.35.Rs Wave scattering processes are characterized by the interaction between an incident wave and a physical obstacle, e.g., light rays scattering off raindrops to form a rainbow and x-ray scattering used in medical imaging. In standard scattering processes, incident waves lose energy due to interaction with the media they traverse. Their incoming amplitude is greater than the amplitude of the reflected waves. However, we know of the existence of some special systems where this behaviour is reversed. The amplitude of the reflected wave is larger than the amplitude of the incoming one, meaning energy is extracted from the system. The most popular examples of this phenomenon, known as superradiance [1], are the scattering of scalar waves by rotating black holes [2,3], and the scattering of electromagnetic waves by a rotating cylinder made of electrical conductive material [4,5].In this paper, we investigate the details behind the phenomenum of superradiance. In our set-up, the wave scattering process is described by a second order differential equation and an effective potential determined by the interaction between the incident wave and the scattering obstacle. We consider a very general potential and derive the necessary and sufficient condition to invoke superradiant wave scattering. Counterintuitively, such scattering only happens in systems where there is absorption, e.g. a electrically conductive rotating cylinder or a rotating black hole. Starting with the standard examples and generalising to other systems, we show that superradiance is possible when the imaginary part of the effective potential is negative. We also demonstrate that the existence of an ergoregion, i.e. a region where no physical observer can remain at rest, is not sufficient for the ocurrence of superradiance; an appropriate boundary condition is also required. We show the relevance of our result for some acoustic spacetime geometries, and point out some misconceptions appearing in the recent literature where an ergoregion was present but the boundary condition was imposed without clear reasoning [6,7]. Finally, we indicate the difference between superradiance and dynam...

Bounding the greybody factors for scalar field excitations on the Kerr-Newman spacetime

“…(See for instance the general discussion by Richartz et al [40].) In the current set-up super-radiance is related to the rotation of the black hole, but if the scalar field additionally carries electric charge there is another contribution to ̟ coming from the electrostatic potential, and so a separate route to super-radiance [18,40].…”

“…(See for instance the general discussion by Richartz et al [40].) In the current set-up super-radiance is related to the rotation of the black hole, but if the scalar field additionally carries electric charge there is another contribution to ̟ coming from the electrostatic potential, and so a separate route to super-radiance [18,40]. While the Dirac equation, being first-order in both space and time, might seem to sidestep this phenomenon, it is a standard result that iterating the Dirac differential operator twice produces a Klein-Gordon-like differential equation.…”

Tidal acceleration of black holes and superradiance

“…[10,12,17]. In absence of a horizon (for example in the case of rotating perfect-fluid stars), regularity boundary conditions must be imposed at the center of the object.…”

Quasinormal modes of black holes: From astrophysics to string theory

“…The existence of an ergoregion is not sufficient for superradiance: An appropriate boundary condition is also necessary, which, for rotating black holes, is the requirement of only the ingoing group velocity waves at the event horizon 317 . When one has the massive scalar or other integer spin field in asymptotically flat or de Sitter space-time or massless field but an AdS boundary at spatial infinity, the superradiance has unstable modes.…”