Astronomy and Astrophysics – Astrophysics – General Relativity and Quantum Cosmology
Scientific paper
1998-02-24
Acta Phys.Polon. B30 (1999) 897-905
Astronomy and Astrophysics
Astrophysics
General Relativity and Quantum Cosmology
final version
Scientific paper
In the spirit of the well-known analogy between inviscid fluids and pseudo-Riemannian manifolds we study spherical singular hypersurfaces in the static superfluid. Such hypersurfaces turn out to be the interfaces dividing the superfluid into the pairs of spherical domains, examples of which are ``superfluid A - superfluid B'' or ``impurity - superfluid'' phases. It is shown that these shells form the acoustic lenses which are the sonic counterparts of the usual optical ones. The exact equations of motion of the lens interfaces are obtained. Also some quantum aspects of the theory are considered. We calculate energy spectra for bound states of acoustic lenses in dynamical equilibrium, taking into account the analogy to a material shell model of a black hole (we consider the cases of spatial topology of a black hole and a wormhole type).
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