Related papers: The Poisson brackets of free null initial data for…

Given a collection of N solutions of the (3+1) vacuum Einstein constraint equations which are asymptotically Euclidean, we show how to construct a new solution of the constraints which is itself asymptotically Euclidean, and which contains…

Global hyperbolicity is a central concept in Mathematical Relativity. Here, we review the different approaches to this concept explaining both, classical approaches and recent results. The former includes Cauchy hypersurfaces, naked…

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}…

We consider a general Euler-Korteweg-Poisson system in $R^3$, supplemented with the space periodic boundary conditions, where the quantum hydrodynamics equations and the classical fluid dynamics equations with capillarity are recovered as…

The classical Poisson reduction of a given Lagrangian system with (local) gauge symmetries has to be done before its quantization. We propose here a coordinate free and self-contained mathematical presentation of the covariant…

We consider the initial data problem for several black holes in vacuum with arbitrary momenta and spins on a three space with punctures. We compactify the internal asymptotically flat regions to obtain a computational domain without inner…

Based on the non-Abelian Lie algebra, a generalized geometric Lie bracket on vector space is proposed to further realize the generalized structural Poisson bracket, and then we briefly discuss the second order equations of the generalized…

The N=1 supersymmetric version of generalized 2d dilaton gravity can be cast into the form of a Poisson Sigma Model, where the target space and its Poisson bracket are graded. The target space consists of a 1+1 superspace and the dilaton,…

Various works have suggested that the Bondi--Sachs--Penrose decay conditions on the gravitational field at null infinity are not generally representative of asymptotically flat space--times. We have made a detailed analysis of the…

A generalization of the theory of algebro-geometric Poisson brackets on the space of finite-gap Schroedinger operators, developped by S. P. Novikov and A. P. Veselov, to the case of periodic zero-diagonal difference operators of second…

We consider an arbitrary Dubrovin-Novikov bracket of degree $k$, namely a homogeneous degree $k$ local Poisson bracket on the loop space of a smooth manifold $M$ of dimension $n$, and show that $k$ connections, defined by explicit linear…

The formalism of hypersurface data is a framework to study hypersurfaces of any causal character abstractly (i.e. without the need of viewing them as embedded in an ambient space). In this paper we exploit this formalism to study the…

We present a detailed analysis of the Hamiltonian constraints of the d-dimensional tetrad-connection gravity where the non-dynamical part of the spatial connection is fixed to zero by an adequate guage transformation. This new action…

We show that the diffeomorphisms, which preserve the null nature for a generic null metric very near to the null surface, provide {\it noncommutative} Heisenberg algebra. This is the generalization of the earlier work (Phys. Rev. D95,…

We discuss the geometry behind classical Heisenberg model at the level suitable for third or fourth year students who did not have the opportunity to take a course on differential geometry. The arguments presented here rely solely on…

Spacetimes with collisionless matter evolving from data on a compact Cauchy surface with hyperbolic symmetry are shown to be timelike and null geodesically complete in the expanding direction, provided the data satisfy a certain size…

We study a nonlinear initial value Cauchy problem depending upon a complex perturbation parameter $\epsilon$ with vanishing initial data at complex time $t=0$ and whose coefficients depend analytically on $(\epsilon,t)$ near the origin in…

The noncommutative space of light-like worldlines that is covariant under the light-like (or null-plane) $\kappa$-deformation of the (3+1) Poincar\'e group is fully constructed as the quantization of the corresponding Poisson homogeneous…

The Null Surface Formulation of General Relativity is developed for 2+1 dimensional gravity. The geometrical meaning of the metricity condition is analyzed and two approaches to the derivation of the field equations are presented. One…

The Lie algebroids are generalization of the Lie algebras. They arise, in particular, as a mathematical tool in investigations of dynamical systems with the first class constraints. Here we consider canonical symmetries of Hamiltonian…