Buracos sônicos em superfícies esféricas - Bernardes, Bruno [UNESP] (2007)
In this dissertation we study the classical aspects of analogue models of General Relativity in condensed matter seeking mainly to create a new perception about semi-classical gravitational eﬀects, such as Hawking radiation, in order to better comprehend them. We demonstrate that sound waves propagating in an ideal barotropic ﬂuid with a non-homogeneous irrotacional ﬂow, over a sphere 'S POT. 2' with radius r behave as a Klein-Gordon massless scalar ﬁeld in a curved spacetime. Through this dissertation, we analyze several properties of this eﬀective spacetime governing the propagation of sound, whose geometry is described by a Lorentzian metric that depends on the hydrodynamic variables of the ﬂow such as the ﬂow velocity, the density and the local speed of sound, always trying to establish correlations between classical concepts of ﬂuid dynamics and purely relativistic concepts. Once a general analysis of these spacetimes is made, which we denominate acoustic spacetimes, we ﬁnd solutions of the dynamic variables of the ﬂuid, since they determine the acoustic geometry, capable of modeling eﬀective spacetimes endowed with event horizons and singularities, creating therefore a dumb/deaf hole, i.e., an analogue of a black hole and white hole of the General Relativity. We further discuss some points of the causal structure of the acoustic spacetimes, so constructing a Carter-Penrose diagram of the dumb/deaf hole with the aim of bringing to evidence the possible null trajectories of this spacetime. Furthermore, we show that in the approximation of the acoustic geometry, also called eikonal approximation, the sound rays follow lightlike geodesics of the acoustic spacetime. Finally we calculate the scalar curvature of this spacetime verifying the presence of the non ﬂat structure of the 'S POT. 2' sphere, over which the ﬂuid moves