Quasi-normal acoustic oscillations in the transonic Bondi flow. (English) Zbl 1332.83014
Summary: We analyze the dynamics of nonspherical acoustic perturbations of the transonic Bondi flow, describing the steady radial accretion of a polytropic perfect fluid into a gravity center. The propagation of such perturbations can be described by a wave equation on the curved effective background geometry determined by the acoustic metric introduced by Unruh in the context of experimental black hole evaporation. We show that for the transonic Bondi flow, Unruh’s acoustic metric describes an analogue black hole and that the acoustic perturbations undergo quasi-normal oscillations. The associated quasi-normal frequencies are computed and they are proven to scale like the surface gravity of the acoustic black hole. This provides an explanation for results given in an earlier work, where it was shown that the acoustic perturbations of a relativistic fluid accreted by a nonrotating black hole possess quasi-normal modes, and where it was found empirically that the associated frequencies scaled like the surface gravity of the analogue black hole in the limit where the radius of the sonic horizon is much larger than the Schwarzschild radius.
MSC:
| 83C05 | Einstein’s equations (general structure, canonical formalism, Cauchy problems) |
| 83C57 | Black holes |
| 83C25 | Approximation procedures, weak fields in general relativity and gravitational theory |
| 76W05 | Magnetohydrodynamics and electrohydrodynamics |
| 83C55 | Macroscopic interaction of the gravitational field with matter (hydrodynamics, etc.) |
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