Related papers: Topology Change in Classical General Relativity

When studying the causal propagation of a field in a globally hyperbolic spacetime M, one often wants to express the physical intuition that it has compact support in spacelike directions, or that its support is a spacelike compact set. We…

We develop causality theory for upper semi-continuous distributions of cones over manifolds generalizing results from mathematical relativity in two directions: non-round cones and non-regular differentiability assumptions. We prove the…

The "trousers" spacetime is a pair of flat 2D cylinders ("legs") merging into into a single one ("trunk"). In spite of its simplicity this spacetime has a few features (including, in particular, a naked singularity in the "crotch") each of…

Restrictions are obtained on the topology of a compact divergence-free null hypersurface in a four-dimensional Lorentzian manifold whose Ricci tensor is zero or satisfies some weaker conditions. This is done by showing that each null…

This paper examines the issue of the existence and nature of time-like geodesics in asymptotically flat spacetimes and proposes a novel generalized topological criterion for the existence of time-like geodesics. Its validity is proved using…

The spacetime of Ho and Weiler [Phys. Rev. D {\bf 87}, 045004 (2013)] supposedly admitting closed timelike curves (CTCs) is flat Minkowski spacetime with a compactified coordinate and can only contain CTCs if the compact direction is chosen…

This paper deals with two aspects of relativistic cosmologies with closed (compact and boundless) spatial sections. These spacetimes are based on the theory of General Relativity, and admit a foliation into space sections S(t), which are…

The conceptual definition and understanding of time, both quantitatively and qualitatively is of the utmost difficulty and importance. As time is incorporated into the proper structure of the fabric of spacetime, it is interesting to note…

We consider a Lorentzian analogue of the Ptolemy inequality and we prove that in the setting of globally hyperbolic spacetimes it is equivalent to a global timelike sectional curvature bound from above by zero. We investigate the link…

For bi-Lipschitz homeomorphisms of a compact manifold it is known that topological entropy is always finite. For compact manifolds of dimension two or greater, we show that in the closure of the space of bi-Lipschitz homeomorphisms, with…

We present a new development of the causal boundary of spacetimes, originally introduced by Geroch, Kronheimer and Penrose. Given a strongly causal spacetime (or, more generally, a chronological set), we reconsider the GKP ideas to…

We consider higher derivative corrections to the graviton three-point coupling within a weakly coupled theory of gravity. Lorentz invariance allows further structures beyond the one present in the Einstein theory. We argue that these are…

The Lott-Sturm-Villani Curvature-Dimension condition provides a synthetic notion for a metric-measure space to have Ricci-curvature bounded from below and dimension bounded from above. We prove that it is enough to verify this condition…

If the topology of the universe is compact we show how it significantly changes our assessment of the naturalness of the observed structure of the universe and the likelihood of its present state of high isotropy and near flatness arising…

Spacetimes in general relativity can be uniquely decomposed into a set of multipole moments. Given the usefulness of moments in the categorization of radiation patterns, tidal deformations, and other phenomena associated with compact…

We propose an exact Hamiltonian lattice theory for (2+1)-dimensional spacetimes with homogeneous curvature. By gauging away the lattice we find a generalization of the ``polygon representation'' of (2+1)-dimensional gravity. We compute the…

We prove a globally hyperbolic spacetime with locally Lipschitz continuous metric and timelike distributional Ricci curvature bounded from below obeys the timelike measure contraction property. The remarkable class of examples of spacetimes…

The causal spacetimes admitting a covariantly constant null vector provide a connection between relativistic and non-relativistic physics. We explore this relationship in several directions. We start proving a formula which relates the…

In this conference published in 1997 some problems on the geodesics of a Lorentzian manifold concerning causality and infinite-dimensional variational methods, are pointed out. Even though a big progress on many of these questions have been…

We propose a topological approach suitable to establish a connection between thermodynamics and topology in the microcanonical ensemble. Indeed, we report on results that point to the possibility of describing {\it interacting classical…