Emergent Spacetimes

Abstract

In this thesis we discuss the possibility that spacetime geometry may be an emergent phenomenon. This idea has been motivated by the Analogue Gravity programme. An "effective gravitational field" dominates the kinematics of small perturbations in an Analogue Model. In these models there is no obvious connection between the "gravitational" field tensor and the Einstein equations, as the emergent spacetime geometry arises as a consequence of linearising around some classical field. After a brief survey of the most relevant literature on this topic, we present our contributions to the field. First, we show that the spacetime geometry on the equatorial slice through a rotating Kerr black hole is formally equivalent to the geometry felt by phonons entrained in a rotating fluid vortex. The most general acoustic geometry is compatible with the fluid dynamic equations in a collapsing/expanding perfect-fluid line vortex. We demonstrate that there is a suitable choice of coordinates on the equatorial slice through a Kerr black hole that puts it into this vortex form; though it is not possible to put the entire Kerr spacetime into perfect-fluid "acoustic" form. We then discuss an analogue spacetime based on the propagation of excitations in a 2-component Bose-Einstein condensate. This analogue spacetime has a very rich and complex structure, which permits us to provide a mass-generating mechanism for the quasi-particle excitations. Additionally, we show that the analogue spacetime based on 2-component Bose-Einstein condensates provides models not just for standard general relativistic spacetimes, but also for the more general bi-metric, and even more general pseudo–Finsler spacetimes. Furthermore, at short distances, where microscopic corrections due to the substructure (i.e., the fundamental Bosons) can no longer be neglected, and even in the mono-metric regime, one begins to see deviations from "Lorentz invariance" — these deviations are qualitatively of the type encountered in "quantum gravity phenomenology", with the interesting property that the Lorentz violating physics is naturally suppressed by powers of the quasi-particle mass divided by the mass of the fundamental bosons that form the condensate. A completely different issue can be probed in a single component BEC. This system naturally exhibits a microscopic mechanism allowing us to perform controlled signature change between Lorentzian and Riemannian geometries. We calculate the number of particles produced from a finite-duration Euclidean signature event, focussing on its impact on particle production in the ultraviolet regime, and the possibility of using the proposed signature change event as an amplifier for pre-existing fluctuations in condensed matter experiments. Last but not least, we investigate cosmological particle production in a Bose-Einstein condensate with tunable microscopic interaction strength. Here Lorentz invariance emerges in the infrared limit, but is explicitly broken in the ultraviolet regime. Thus these models are similar to many (but not, all) models of quantum gravity, where a breakdown of Lorentz invariance is expected for ultraviolet physics around the Planck/string scale. Motivated by previous studies on spacetimes emerging from a microscopic substrate, we show how these modifications naturally lead to momentum-dependent rainbow metrics. In detail we investigate the robustness of the particle production process against the model-specific modifications, and also encounter cosmological particle production in "rainbow inflation". We conclude with a brief discussion of lessons learned from these emergent spacetime models.