Buraco negro acústico e efeito Aharonov-Bohm análogo.

Abstract

In this dissertation we studied an analogue model of gravitation introduced by William George Unruh in 1981, known as an acoustic black hole based on the propagation of sound in a superuid. We verify the behavior of theuid equations in a draining bathtub, where it is possible to study phenomena that occur in a black hole, such as those described by Kerr in general relativity. The work begins with a review on acoustic black holes describing the metric for this case, followed by a study on the Aharonov-Bohm e ect where we analyze the scattering theory for this effect. We also present an analysis of the acoustic metric, for a draining bathtub, from the asymptotic conditions we nd the analytical solution for the radial equation obtained from the metric. With theseresults we studied phenomena such as superradiance, scattering and di erential scatteringcross section by a draining vortex, comparing these results with the scattering obtained for the Aharonov-Bohm e ect. We perform a numerical analysis, where it is possible to check these effects graphically. Considering the Abelian Higgs model with terms of high derivatives, we set up a new metric and considering the non-relativistic case, wend that the differential scattering cross section and the absorption are modi ed by an extra term.