Again, these processes have a purely kinematical origin, so they are perfectly suitable for being reproduced in an analogue model. Regarding these processes, the simplest geometry that one can reproduce, thinking of analogue models based on fluid flows, is that of the draining bathtub of Section 2. Of course, this metric does not exactly correspond to Kerr geometry, nor even to a section of it [641, 633]. However, it is qualitatively similar. It can be used to simulate both Penrose’s classical process and quantum super-radiance, as these effects do not depend on the specific multipole decomposition of Kerr’s geometry, but only on its rotating character. A specific experimental setup has been put forward by Schützhold and Unruh using gravity waves in a shallow basin mimicking an ideal draining bathtub . Equivalent to what happens with Kerr black holes, this configuration is classically stable in vacuum (in the linear regime) . A word of caution is in order here: Interactions of the gravity surface waves with bulk waves (neglected in the analysis) could cause the system to become unstable . This instability has no counterpart in standard general relativity (though it might have one in braneworld theories). Super-resonant scattering of waves in this rotating sink configuration, or in a simple purely rotating vortex, could in principle be observed in this and other analogue models. There are already several articles dealing with this problem [55, 57, 56, 112, 193, 392]. Most recently, see , where necessary and sufficient conditions for super-radiance were investigated.
A related phenomenon one can consider is the black-hole bomb mechanism . One would only have to surround the rotating configuration by a mirror for it to become grossly unstable. What causes the instability is that those in-going waves that are amplified when reflected in the ergosphere would then in turn be reflected back toward the ergoregion, due to the exterior mirror, thus being amplified again, and so on.
An interesting phenomenon that appears in many condensed matter systems is the existence of quantised vortices. The angular momentum of these vortices comes in multiples of some fundamental unit (typically or something proportional to ). The extraction of rotational energy by a Penrose process in these cases could only proceed via finite-energy transitions. This would supply an additional specific signature to the process. In such a highly quantum configuration, it is also important to look for the effect of having high-energy dispersion relations. For example, in BECs, the radius of the ergoregion of a single quantised vortex is on the order of the healing length, so one cannot directly associate an effective Lorentzian geometry with this portion of the configuration. Any analysis that neglects the high-energy terms is not going to give any sensible result in these cases.
Living Rev. Relativity 14, (2011), 3
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