On the analogy between black holes and bathtub vortices - Patrick, Sam (2019)
Analogical thinking is a valuable tool in theoretical physics, since it allows us to take the understanding we have developed in one system and apply it to another. In this thesis, we study the analogy between two seemingly unlikely systems: rotating black holes, elusive cosmic entities that push our theoretical understanding of modern physics to its limits, and bathtub vortices, an occurrence so common that they can be observed on a day-to-day basis in almost any household. Despite the clear difference between these two systems, we argue that lessons from each can be used to learn something about the other. We investigate the equivalence between surface wave propagation in shallow water and the propagation of a massless scalar field on an effective spacetime, focussing in particular on the rotating black hole geometry sourced by a rotating draining vortex flow. Using this analogy, we verify for the first time that three effects predicted to occur around rotating black holes also occur in a laboratory experiment. These are superradiance, an energy enhancement process whereby waves extract rotational energy from the system, quasi-normal ringing, describing the relaxation of the system toward equilibrium, and the backreaction, which mediates the exchange of energy between fluctuations and the background they experience. Previous studies within analogue gravity have focussed on demonstrating that the existence of Hawking radiation does not depend on the details of high frequency dispersion. Our experimental results indicate that the same can be said for superradiance and quasi-normal ringing, although notable differences do occur when the medium is dispersive. Using tools originally developed in the context of black hole physics, we propose a new method for flow measurement based on the characteristic ringing frequencies of the vortex, which can be used for a known effective field theory to measure the parameters of the fluid flow, or for known flow parameters to test the effective field theory. We also study how the characteristic mode spectrum is modified by a purely rotating fluid with vorticity, finding that the system can also support bound state resonances characterised by a much longer lifetime than the usual modes. Finally, we demonstrate theoretically and experimentally how the backreaction of waves onto the background flow manifests itself in the bathtub system. This study reveals several interesting features of experimental bathtub vortices, in particular that the presence of waves leads to the removal of fluid mass from the system, leading to a net decrease in the water level. This dynamical interplay between waves and the background makes it a promising candidate for study in the quantum regime, where the spontaneous emission of waves will also influence the system's evolution.