Related papers: Celestial Holography: Lectures on Asymptotic Symme…
We describe asymptotic symmetries at spatial infinity of asymptotically flat spacetimes within the context of a generalization of the Beig-Schmidt-Ashtekar-Romano-framework. We demonstrate that it is possible to relax certain smoothness…
A longstanding question in quantum gravity regards the localization of quantum information; one way to formulate this question is to ask how subsystems can be defined in quantum-gravitational systems. The gauge symmetry and necessity of…
The alignments between galaxies, their underlying matter structures, and the cosmic web constitute vital ingredients for a comprehensive understanding of gravity, the nature of matter, and structure formation in the Universe. We provide an…
This paper is a sequel to one in which we examined the affine symmetry algebras of arbitrary classical principal chiral models and symmetric space models in two dimensions. It examines the extension of those results in the presence of…
In this paper we analyze in detail a collection of motivating examples to consider $b^m$-symplectic forms and folded-type symplectic structures. In particular, we provide models in Celestial Mechanics for every $b^m$-symplectic structure.…
We study the concentration of ladder sequences of spherical harmonics on caustic latitude circles. We prove that they have Airy scaling asymptotics. We also determine the weak* limit of certain empirical measures of $L^2$ norms of…
The mapping between bulk supergravity fields in anti-de Sitter space and operators in the dual boundary conformal field theory usually relies heavily on the available global symmetries. In the present work, we study a generalization of this…
An overview is provided of the singularity theorems in cosmological contexts at a level suitable for advanced graduate students. The necessary background from tensor and causal geometry to understand the theorems is supplied, the…
These are expanded lecture notes of a mini-course whose objectives were to introduce the basic concepts, constructions and techniques of noncommutative geometry, as well as their uses as a framework for modelling quantum spacetime. Key…
Several issues related to the gravitational clustering of collisionless dark matter in an expanding universe is discussed. The discussion is pedagogical but the emphasis is on semianalytic methods and open questions - rather than on well…
We present a new gauge for asymptotically flat spacetime that can treat future and past null infinities ($\mathscr{I}^{+}$ or $\mathscr{I}^{-}$) democratically. Our gauge is complementary to Bondi and Ashtekar-Hansen gauges, and is adapted…
We analyze the asymptotic symmetries and their associated charges at spatial infinity in $4$-dimensional asymptotically-flat spacetimes. We use the covariant formalism of Ashtekar and Hansen where the asymptotic fields and symmetries live…
A general relativistic description of a disk rotating at constant angular velocity is given. It is argued that conceptually this direct approach poses fewer problems than the special relativistic one. For observers on the disk, the geometry…
We explore the holographic principle in the context of asymptotically flat space-times by means of the asymptotic symmetry group of this class of space-times, the so called Bondi-Metzner-Sachs (BMS) group. In particular we construct a…
A systematic asymptotic expansion is developed for the gravitational wave degrees of freedom of a class of expanding, vacuum Gowdy cosmological spacetimes. In the wave map description of these models, the evolution of the gravitational wave…
The asymptotic expansion method is generalized from the periodic setting to stationary ergodic stochastic geometries. This will demonstrate that results from periodic asymptotic expansion also apply to non-periodic structures of a certain…
In this paper we survey several intersection and non-intersection phenomena appearing in the realm of symplectic topology. We discuss their implications and finally outline some new relations of the subject to algebraic geometry.
We discuss some recent results in the quest to implement the holographic principle in asymptotically flat spacetimes. In particular we introduce the key ingredients of the candidate dual theory which lives at null infinity and it is…
Asymptotic cones are structures that encode how a metric space appears when seen from far away. We discuss their meaning and potential significance for quantum gravity.
Dynamical electro-weak symmetry breaking is an appealing, strongly-coupled alternative to the weakly-coupled models based on an elementary scalar field developing a vacuum expectation value. In the first two sections of this set of…