Related papers: Gluing constructions for Lorentzian length spaces
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…
We establish the Lorentzian AdS$_2$/CFT$_1$ correspondence from a reconstruction of all bulk points through the kinematic-space approach. The OPE block is exactly a bulk local operator. We formulate the correspondence between the bulk…
In this chapter we describe a selection of mathematical techniques and results that suggest interesting links between the theory of gratings and the theory of homogenization, including a brief introduction to the latter. By no means do we…
We use the intrinsic area to define a distance on the space of homothety classes of convex bodies in the $n$-dimensional Euclidean space, which makes it isometric to a convex subset of the infinite dimensional hyperbolic space. The ambient…
The standard definition of gravitational lensing magnification is generalized to Lorentzian spacetimes, and it is shown how it can be interpreted geometrically in terms of the van Vleck determinant and the exponential map. This is joint…
The constructive method of conformal blocks is developed for the construction of global solutions for two-dimensional metrics having one Killing vector. The method is proved to yeild a smooth universal covering space with a smooth…
We present in this paper the formalism for the splitting of a four-dimensional Lorentzian manifold by a set of time-like integral curves. Introducing the geometrical tensors characterizing the local spatial frames induced by the congruence…
We introduce the blockwise gluing construction. This describes residuated integral chains which can be decomposed into (possibly) partial algebras, stacked one on top of the other, and such that elements in a certain component multiply in…
The AdS/CFT correspondence, or more generally the gauge/gravity duality, is a remarkable conjecture obtained from superstring theory with various D-brane backgrounds. According to this conjecture, a higher-dimensional curved space-time…
The paper introduces the class of O-metric spaces, a novel generalization of metric-type spaces, classifying almost all possible metric types into upward and downward O-metrics. We list some topologies arising from O-metrics and discuss…
We show how to exploit symmetry assumptions to determine the dynamical equations for the particular geometry that underpins given matter field equations. The procedure builds on the gravitational closure equations for matter models without…
In this work we construct a sequence of Riemannian metrics on the three-sphere with scalar curvature greater than or equal to $6$ and arbitrarily large widths. Our procedure is based on the connected sum construction of positive scalar…
We first prove a general gluing theorem which creates new nondegenerate constant mean curvature surfaces by attaching half Delaunay surfaces with small necksize to arbitrary points of any nondegenerate CMC surface. The proof uses the method…
The lattice gauge theory for curved spacetime is formulated. A discretized action is derived for both gluon and quark fields which reduces to the generally covariant form in the continuum limit. Using the Wilson action, it is shown…
We develop a ``canonical Wick rotation-rescaling theory in 3-dimensional gravity''. This includes: (a) A simultaneous classification that shows how generic maximal globally hyperbolic spacetimes of constant curvature, which admit a complete…
The comparison theory for the Riccati equation satisfied by the shape operator of parallel hypersurfaces is generalized to semi-Riemannian manifolds of arbitrary index, using one-sided bounds on the Riemann tensor which in the Riemannian…
We construct initial data sets which satisfy the vacuum constraint equa- tions of General Relativity with positive cosmologigal constant. More pre- silely, we deform initial data with ends asymptotic to Schwarzschild-de Sitter to obtain…
We provide an explicit procedure to glue (not necessarily compact) silting objects along recollements of triangulated categories with coproducts having a 'nice' set of generators, namely, well generated triangulated categories. This…
We apply tilting theory over preprojective algebras $Lambda$ to a study of moduli space of $Lambda$-modules. We define the categories of semistable modules and give an equivalence, so-called reflection functors, between them by using…
We prove the equivalence of two seemingly very different ways of generalising Rademacher's theorem to metric measure spaces. One such generalisation is based upon the notion of forming partial derivatives along a very rich structure of…