Conditional probabilities in Ponzano-Regge minisuperspace

We examine the Hartle-Hawking no-boundary initial state for the Ponzano-Regge formulation of gravity in three dimensions. We consider the behavior of conditional probabilities and expectation values for geometrical quantities in this initial state for a simple minisuperspace model consisting of a two-parameter set of anisotropic geometries on a 2-sphere boundary. We find dependence on the cutoff used in the construction of Ponzano-Regge amplitudes for expectation values of edge lengths. However, these expectation values are cutoff independent when computed in certain, but not all, conditional probability distributions. Conditions that yield cutoff independent expectation values are those that constrain the boundary geometry to a finite range of edge lengths. We argue that such conditions have a correspondence to fixing a range of local time, as classically associated with the area of a surface for spatially closed cosmologies. Thus these results may hint at how classical spacetime emerges from quantum amplitudes.Comment: 26 pages including 10 figures, some reorganization in the presentation of results, expanded discussion of results in the context of 2+1 gravity in the Witten variables, 3 new reference

Towards the Final Fate of an Unstable Black String

Black strings, one class of higher dimensional analogues of black holes, were shown to be unstable to long wavelength perturbations by Gregory and Laflamme in 1992, via a linear analysis. We revisit the problem through numerical solution of the full equations of motion, and focus on trying to determine the end-state of a perturbed, unstable black string. Our preliminary results show that such a spacetime tends towards a solution resembling a sequence of spherical black holes connected by thin black strings, at least at intermediate times. However, our code fails then, primarily due to large gradients that develop in metric functions, as the coordinate system we use is not well adapted to the nature of the unfolding solution. We are thus unable to determine how close the solution we see is to the final end-state, though we do observe rich dynamical behavior of the system in the intermediate stages.Comment: 17 pages, 7 figure

Conditional probabilities in the quantum cosmology of Ponzano-Regge theory

We examine the discrete Ponzano-Regge formulation of (2+1)-dimensional gravity in the context of a consistent histories approach to quantum cosmology. We consider 2- dimensional boundaries of a 3-dimensional spacetime. The 2-dimensional boundaries are tessellated as the surface of a single tetrahedron. Two classes of the tetrahedral tessellation are considered—the completely isotropic tetrahedron and the two-parameter anisotropic tetrahedron. Using Ponzano-Regge wavefunctions, we calculate expectation values and uncertainties for the edge lengths of these tetrahedra. In doing so, we observe finite size effects in the expectation values and uncertainties when the calculations fail to constrain the space of histories accessible to the system. There is, however, an indication that the geometries of the tetrahedra (as quantified by the ratios of their edge lengths) freeze out with increasing cutoff. Conversely, cutoff invariance is observed in our calculations provided the space of histories is constrained by an appropriate fixing of the tetrahedral edge lengths. It is thus suggested that physically meaningful results regarding the early state of our universe can be obtained providing we formulate the problem in a careful manner. A few of the difficulties inherent in quantum cosmology are thereby addressed in this study of an exactly calculable theory.Science, Faculty ofPhysics and Astronomy, Department ofGraduat

Maxwell-Klein-Gordon fields in black hole spacetimes

In this thesis I present results for the evolution and dynamics of massive electromagnetically coupled Maxwell-Klein-Gordon fields in black hole spacetimes. The first part of my investigation for gravitationally and electromagnetically self-interacting fields in spherical symmetry reveals two distinct types of solution at the threshold of black hole formation. For fields with relatively small mass parameter I observe Type II discretely self-similar behaviour for the critical solutions and obtain the black hole mass and charge scaling relations. However, when the mass parameter is sufficiently large a different type of critical solution is obtained.. This new solution is periodic and resembles a perturbed charged boson star solution. This new solution exhibits Type I critical behaviour and its lifetime obeys a well-defined scaling law. The second aspect of investigation involves massive electromagnetically coupled scalar field perturbations in axial symmetry on a Kerr black hole spacetime. Here, results show that both the mass and charge coupling parameters play a significant role in the field dynamics on the spacetime background. For relatively weak parameter values the perturbations exhibit strong gravitational interaction through the phenomenon of orbiting resonances. In the case of pure electromagnetic perturbation there is also evidence of superradiant scattering when the black hole rotation is large. When the parameter values are large both the physics and complexity of the dynamics change. For intermediate values of the mass and charge parameter, the perturbations exhibit trapping and a preference for scattering along the axis of black hole rotation. Finally, all electromagnetically coupled solutions generically display charge separation and dynamo-like behaviour.Science, Faculty ofPhysics and Astronomy, Department ofGraduat