Related papers: A note on spacelike and timelike compactness
The definitions of global hyperbolicity for closed cone structures and topological preordered spaces are known to coincide. In this work we clarify the connection with definitions of global hyperbolicity proposed in recent literature on…
Two theorems related to gravitational time delay are proven. Both theorems apply to spacetimes satisfying the null energy condition and the null generic condition. The first theorem states that if the spacetime is null geodesically…
In this work, we prove a compactness theorem on the space of all Hamiltonian stationay Lagrangian submanifolds in a compact symplectic manifold with uniform bounds on area and total extrinsic curvature.
We study the existence of surfaces with constant or prescribed Gauss curvature in certain Lorentzian spacetimes. We prove in particular that every (non-elementary) 3-dimensional maximal globally hyperbolic spatially compact spacetime with…
Let (M,g) be a compact Riemannian three-dimensional manifold with boundary. We prove the compactness of the set of scalar-flat metrics which are in the conformal class of g and have the boundary as a constant mean curvature hypersurface.…
We address problems associated with compactification near and on the light front. In perturbative scalar field theory we illustrate and clarify the relationships among three approaches: (1) quantization on a space-like surface close to a…
Let $S$ be a closed surface of hyperbolic type. We show that, for every pair $(g_+,g_-)$ of negatively curved metrics over $S$ there exists a unique GHMC Minkowski spacetime $X$ into which $(S,g_+)$ and $(S,g_-)$ isometrically embed as…
In this article we present a review of a geometric and algebraic approach to causal cones and describe cone preserving transformations and their relationship with the causal structure related to special and general relativity. We describe…
In this article we inspect the dynamics of classical field theories with a local conformal behavior. Our interest in the multisymplectic setting comes from its suitable description of field theories, and the conformal character has been…
Given a spacelike foliation of a spacetime and a marginally outer trapped surface S on some initial leaf, we prove that under a suitable stability condition S is contained in a ``horizon'', i.e. a smooth 3-surface foliated by marginally…
We present a short review of geometric and algebraic approach to causal cones and describe cone preserving transformations and their relationship with causal structure related to special and general theory of relativity. We describe Lie…
We consider expanding vacuum spacetimes with a CMC foliation by compact spacelike hypersurfaces. Under scale invariant a priori geometric bounds (type-III), we show that there are arbitrarily large future time intervals that are modelled by…
Let $G$ be a connected semi-simple algebraic group of adjoint type over an algebraically closed field, and let $\overline{G}$ be the wonderful compactification of $G$. For a fixed pair $(B, B^-)$ of opposite Borel subgroups of $G$, we look…
In [8] Gerhardt proves longtime existence for the inverse mean curvature flow in globally hyperbolic Lorentzian manifolds with compact Cauchy hypersurface, which satisfy three main structural assumptions: a strong volume decay condition, a…
We study five-dimensional Kasner cosmologies in the vicinity of a conifold locus occurring in a time-dependent Calabi-Yau compactification of M-theory. The dynamics of M2-brane winding modes, which become light in this region, is taken into…
I give a brief informal introduction to the idea and tests of large extra dimensions, focusing on the case in which the space-time manifold has a direct product structure. I then describe some attractive implementations in which the…
We prove that a globally hyperbolic spacetime with its causality relation is a bicontinuous poset whose interval topology is the manifold topology. This provides an abstract mathematical setting in which one can study causality independent…
We consider the Cauchy problem with smooth data for compressible Euler equations in many dimensions and concentrate on two cases: solutions with finite mass and energy and solutions corresponding to a compact perturbation of a nontrivial…
We study contracting curvature flows of compact hypersurfaces with positive sectional curvature in hyperbolic space $\mathbb{H}^{n+1}$. The speed is assumed to be homogeneous of degree one in the principal curvatures and to satisfy certain…
It is generally known that linear (free) field theories are one of the few QFT that are exactly soluble. In the Schroedinger functional description of a scalar field on flat Minkowski spacetime and for flat embeddings, it is known that the…