2005

Ph.D

University of Madras

Using the analogy between a shrinking fluid vortex (drain bath tub) modelled as a (2+1)-dimensional fluid flow with a sink at the origin, and a rotating black hole with an ergosphere, it is shown that a scalar sound wave is reflected from such a vortex with an amplification for a specific range of frequencies of the incident wave depending on the angular velocity of rotation of the vortex. This thesis also investigates superresonant scattering of acoustic disturbances from a rotating acoustic black hole in the low frequency range. The idea of superradiance scattering originated from Penrose's proposal of extracting energy from black holes. One can extract energy from a black hole if it has angular momentum, due to the fact that in the case of rotating black hole there exists a region of spacetime, outside the blackhole where time translational killing vector becomes spacelike and hence a test particle can have either positive or negative energy in that region of spacetime. The process of superradiance scattering is purely kinematic since it does not involve Einstein's equation to show that the rotating black holes superradiate. The first part of this thesis investigates the possibility of the acoustic analog of superradiance, the amplification of a sound wave by reflection from the ergoregion of a rotating acoustic black hole. The so-called 'draining bath tub' of fluid flow, which is basically a (2+1) dimensional flow is chosen with a sink at the origin. It has been shown that linear acoustic perturbations scatter form the ergo region with an enhancement in amplitude, for a restricted range of frequencies of the incoming wave. An explicit expression is derived for the reflection coefficient as a function of the frequency of the incoming wave for a certain low frequency regime which is expected to be useful for possible feature experimental endeavours to observe superresonance. Based on the work, 'when a sound wave passes by an irrotational vortex, its trajectory is bent', by Fischer and Visser, the author has demonstrated, the bending of a sound wave for a spiral flow (vortex with sink) of the fluid, using differential geometric techniques, as used in general Relativity. This analysis is valid when wavelength is very small compared to the typical scale of variation of the acoustic geometry. The acoustic analog models of gravity is discussed; Different stationary solutions of Einstein's equation are described; Bending of light and corresponding time delay in Schwarzchild geometry is discussed. Bending of a Phonon in acoustic geometry and the corresponding time delay is demonstrated.