Related papers: Causal structure and degenerate phase boundaries

Ashtekar's formulation for canonical quantum gravity is known to possess the topological solutions which have their supports only on the moduli space $\CN$ of flat $SL(2,C)$ connections. We show that each point on the moduli space $\CN$…

Cahn-Hilliard models are central for describing the evolution of interfaces in phase separation processes and free boundary problems. In general, they have non-constant and often degenerate mobilities. However, in the latter case, the…

We give an up-to-date perspective with a general overview of the theory of causal properties, the derived causal structures, their classification and applications, and the definition and construction of causal boundaries and of causal…

In this article we propose a new geometrization of the radiative phase space of asymptotically flat space-times: we show that the geometry induced on null-infinity by the presence of gravitational waves can be understood to be a…

A recently proposed algebraic representation of the causal set model of the small-scale structure of space-time of Sorkin et al. is briefly reviewed and expanded. The algebraic model suggested, called quantum causal set, is physically…

In this paper, we study the linear wave equations in an asymptotically anti-de Sitter spacetime. We will consider the mixed boundary problem, where the initial data are given on an outgoing null hypersurface and a timelike hypersurface, and…

One studies certain degenerations of the generic square matrix over a field $k$ along with its main related structures, such as the determinant of the matrix, the ideal generated by its partial derivatives, the polar map defined by these…

Dynamical systems whose symplectic structure degenerates, becoming noninvertible at some points along the orbits are analyzed. It is shown that for systems with a finite number of degrees of freedom, like in classical mechanics, the…

This continuum mechanical theory aims at detailing the underlying rational mechanics of dynamic boundary conditions proposed by Fischer, Maass, & Dieterich [1], Goldstein, Miranville, & Schimperna [2], and Knopf, Lam, Liu & Metzger, [3]. As…

We examine the reduced phase space of the Barbero-Varadarajan solutions of the Ashtekar formulation of (2+1)-dimensional general relativity on a torus. We show that it is a finite-dimensional space due to existence of an infinite…

Spacetime must be foliable by spacelike surfaces for the quantum mechanics of matter fields to be formulated in terms of a unitarily evolving state vector defined on spacelike surfaces. When a spacetime cannot be foliated by spacelike…

In asymptotically free theories with collinear divergences it is sometimes claimed that these divergences cancel if one sums over initial and final state degenerate cross-sections and uses an off-shell renormalisation scheme. We show for…

This article is concerned with causal structures, which are defined as a field of tangentially non-degenerate projective hypersurfaces in the projectivized tangent bundle of a manifold. The local equivalence problem of causal structures on…

When one studies the Casimir effect, the periodic (anti-periodic) boundary condition is usually taken to mimic a periodic (anti-periodic) structure for a scalar field living in a flat space with a non-Euclidean topology. However, there…

The isolated horizon formalism recently introduced by Ashtekar et al. aims at providing a quasi-local concept of a black hole in equilibrium in an otherwise possibly dynamical spacetime. In this formalism, a hierarchy of geometrical…

The new formulation of the causal completion of spacetimes suggested in [1], and modified later in [2], is tested by computing the causal boundary for product spacetimes of a Lorentz interval and a Riemannian manifold. This is…

Given a time function $\tau$ on a spacetime $M$, we define a `null distance function', $\hat{d}_\tau$, built from and closely related to the causal structure of $M$. In basic models with timelike $\nabla \tau$, we show that 1)…

It is shown that Kundt's metric for vacuum cannot be constructed when two-dimensional space-like sections of null hypersurfaces are compact, connected manifolds with no boundary unless they are tori or spheres, i.e. higher genus $\mathbf{g}…

Gapped phases with long-range entanglement may admit gapped boundaries. If the boundary is gapped, the ground-state degeneracy is well-defined and can be computed using methods of Topological Quantum Field Theory. We derive a general…

We show that every point in a uniformly $2$-nondegenerate CR hypersurface is canonically associated with a model $2$-nondegenerate structure. The $2$-nondegenerate models are basic CR invariants playing the same fundamental role as quadrics…