Four-dimensional, asymptotically flat spacetimes with an ergoregion but no horizon have been shown to be linearly unstable against a superradiant-triggered mechanism. This result has wide implications in the search for astrophysically viable alternatives to black holes, but also in the understanding of black holes and Hawking evaporation. Here we investigate this instability in detail for a particular setup which can be realized in the laboratory: the {\it hydrodynamic vortex}, an effective geometry for sound waves, with ergoregion and without an event horizon.Comment: 10 pages, 8 figures, 2 table
We analyze the tidal forces produced in the spacetime of Reissner-Nordström black holes. We point out that the radial component of the tidal force changes sign just outside the event horizon if the charge-to-mass ratio is close to 1 unlike in Schwarzschild spacetime of uncharged black holes, and that the angular component changes sign between the outer and inner horizons. We solve the geodesic deviation equations for radially falling bodies towards the charged black hole. We find, for example, that the radial component of the geodesic deviation vector starts decreasing inside the event horizon unlike in the Schwarzschild case.
Under certain conditions, sound waves in a fluid may be governed by a Klein-Gordon equation on an `effective spacetime' determined by the background flow properties. Here we consider the draining bathtub: a circulating, draining flow whose effective spacetime shares key features with the rotating black hole (Kerr) spacetime. We present a complete investigation of the role of quasinormal (QN) mode and Regge pole (RP) resonances of this system. First, we simulate a perturbation in the time domain by applying a finite-difference method, to demonstrate the ubiquity of `QN ringing'. Next, we solve the wave equation in the frequency domain with the continued-fraction method, to compute QN and RP spectra numerically. We then explore the geometric link between (prograde and retrograde) null geodesic orbits on the spacetime, and the properties of the QN/RP spectra. We develop a `geodesic expansion' method which leads to asymptotic expressions (in inverse powers of mode number $m$) for the spectra, the radial functions and the residues. Next, the role of the Regge poles in scattering and absorption processes is revealed through application of the complex angular momentum method. We elucidate the link between the Regge poles and oscillations in the absorption cross section. Finally, we show that Regge poles provide a neat explanation for `orbiting' oscillations seen in the scattering cross section.Comment: 18 pages, 9 figures, 1 table. Added a new section on Regge Pole residues and `orbiting' oscillations in scattering cross section
Analogue systems are a powerful instrument to investigate and understand in a controlled setting many general-relativistic effects. Here, we focus on superradiant-triggered instabilities and quasi-normal modes. We consider a compressible hydrodynamic vortex characterized by a polytropic equation of state, the {\it polytropic hydrodynamic vortex}, a purely circulating system with an ergoregion but no event horizon. We compute the quasinormal modes of this system numerically with different methods, finding excellent agreement between them. When the fluid velocity is larger than the speed of sound, an ergoregion appears in the effective spacetime, triggering an "ergoregion instability." We study the details of the instability for the polytropic vortex, and in particular find analytic expressions for the marginally-stable configuration.Comment: 11 pages, 3 figures, 5 table
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