Related papers: Topology change with Morse functions: progress on …
Studies in 1+1 dimensions suggest that causally discontinuous topology changing spacetimes are suppressed in quantum gravity. Borde and Sorkin have conjectured that causal discontinuities are associated precisely with index 1 or n-1 Morse…
Morse spacetime is a model of singular Lorentzian manifold, built upon a Morse function which serves as a global time function outside its critical points. The Borde-Sorkin conjecture states that a Morse spacetime is causally continuous if…
The result that, for a scalar quantum field propagating on a ``trousers'' topology in 1+1 dimensions, the crotch singularity is a source for an infinite burst of energy has been used to argue against the occurrence of topology change in…
The role of topology in elementary quantum physics is discussed in detail. It is argued that attributes of classical spatial topology emerge from properties of state vectors with suitably smooth time evolution. Equivalently, they emerge…
We consider certain interesting processes in quantum gravity which involve a change of spatial topology. We use Morse theory and the machinery of handlebodies to characterise topology changes as suggested by Sorkin. Our results support the…
A change of spatial topology in a causal, compact spacetime cannot occur when the metric is globally Lorentzian. One can however construct a causal metric from a Riemannian metric and a Morse function on the background cobordism manifold,…
We study topology change in (2+1)D gravity coupling with non-Abelian SO(2,1) Higgs field from the point of view of Morse theory. It is shown that the Higgs potential can be identified as a Morse function. The critical points of the latter…
A review is given of recent work on topology changing solutions to the first order form of general relativity. These solutions have metrics which are smooth everywhere, invertible almost everywhere, and have bounded curvature. The…
The spin-statistics connection, quantum gravity and other physical considerations suggest that classical space-time topology is not an immutable attribute and can change in quantum physics. The implementation of topology change using…
This dissertation presents a semiclassical analysis of conical topology change in $1+1$ spacetime dimensions wherein, to lowest order, the ambient spacetime is classical and fixed while the scalar field coupled to it is quantized. The…
This paper clarifies some aspects of Lorentzian topology change, and it extends to a wider class of spacetimes previous results of Geroch and Tipler that show that topology change is only to be had at a price. The scenarios studied here are…
In this paper we study topology-changing spacetimes occurring from pointlike sources. Following an old idea of Penrose, we will opt for a non-Hausdorff model of topology change in which an initial pointlike source is ``doubled" and allowed…
The role of topology change in a fundamental theory of quantum gravity is still a matter of debate. However, when regarding string theory as two-dimensional quantum gravity, topological fluctuations are essential. Here we present a third…
Classical Morse theory proceeds by considering sublevel sets $f^{-1}(-\infty, a]$ of a Morse function $f: M \to R$, where $M$ is a smooth finite-dimensional manifold. In this paper, we study the topology of the level sets $f^{-1}(a)$ and…
The non-classical features of quantum mechanics are reproduced using models constructed with a classical theory - general relativity. The inability to define complete initial data consistently and independently of future measurements,…
Two singularity theorems can be proven if one attempts to let a Lorentzian cobordism interpolate between two topologically distinct manifolds. On the other hand, Cartier and DeWitt-Morette have given a rigorous definition for quantum field…
Emergent gravity is based on the Darboux theorem or the Moser lemma in symplectic geometry stating that the electromagnetic force can always be eliminated by a local coordinate transformation as far as U(1) gauge theory is defined on a…
In this thesis we analyze a very simple model of two dimensional quantum gravity based on causal dynamical triangulations (CDT). We present an exactly solvable model which indicates that it is possible to incorporate spatial topology…
In these two lectures I describe the difficulties one encounters when trying to construct a framework in which to describe topology change in classical general relativity where one sticks to the assumption of an everywhere non-singular…
A local criterion of topological phase transitions is established based on the Morse theory: a topological phase transition occurs when the count of Morse critical points of the order function changes. The locations in space where this…