Related papers: Transformations of Asymptotically AdS Hyperbolic I…
It is natural to regulate an infinite-sized system by imposing a boundary condition at finite distance, placing the system in a "box." This breaks symmetries, though the breaking is small when the box is large. One should thus be able to…
The calculation of conserved charges of black holes is a rich problem, for which many methods are known. Until recently, there was some controversy on the proper definition of conserved charges in asymptotically anti-de Sitter (AdS) spaces…
An averaging method for getting uniformly valid asymptotic approximations of the solution of hyperbolic systems of equations is presented. The averaged system of equations disintegrates into independent equations for non-resonance systems.…
General Relativity in 4 dimensions can be equivalently described as a dynamical theory of SO(3)-connections rather than metrics. We introduce the notion of asymptotically hyperbolic connections, and work out an analog of the…
In recent years, there has been considerable interest in theories formulated in anti-de Sitter (AdS) spacetime. However, AdS spacetime fails to be globally hyperbolic, so a classical field satisfying a hyperbolic wave equation on AdS…
In this paper we focus on the initial value problem for a hyperbolic-elliptic coupled system of a radiating gas in multi-dimensional space. By using a time-weighted energy method, we obtain the global existence and optimal decay estimates…
We consider hyperbolic equations with time-dependent coefficients and develop an abstract framework to derive the asymptotic behaviour of the representation of solutions for large times. We are dealing with generic situations where the…
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…
We perform a numerical simulation of the evolution of inhomogeneities with transverse profile in a collision of gravitational shockwaves in asymptotically anti-de Sitter spacetime. This constitutes a step closer towards an accurate…
In this paper, the notion of hyperbolic ellipsoids in hyperbolic space is introduced. Using a natural orthogonal projection from hyperbolic space to Euclidean space, we establish affine isoperimetric type inequalities for static convex…
To study asymptotic structures, we regularize Einstein's field equations by means of conformal transformations. The conformal factor is chosen so that it carries a dimensional scale that captures crucial asymptotic features. By choosing a…
We study the conserved charges of supersymmetric solutions in the topologically massive gravity theory for both asymptotically flat and constant curvature geometries.
For an asymptotically flat initial-data set in general relativity, the total mass-momentum may be interpreted as a Hermitian quadratic form on the complex, two-dimensional vector space of ``asymptotic spinors''. We obtain a generalization…
We show that $3$-dimensional AdS spacetime can be semiclassically unstable due to strongly interacting quantum field effects. In our previous paper, we have pointed out the possibility of such an instability of AdS$_3$ by inspecting linear…
This article uses the conformal Einstein equations and the conformal representation of spatial infinity introduced by Friedrich to analyse the behaviour of the gravitational field near null and spatial infinity for the development of…
We develop a min-max theory for certain complete minimal hypersurfaces in hyperbolic space. In particular, we show that given two strictly stable minimal hypersurfaces that are both asymptotic to the same ideal boundary, there is a new one…
In this talk we shall show a perfect fluid cosmological model and its properties. The model possesses an orthogonally transitive abelian two-dimensional group of isometries that corresponds to cylindrical symmetry. The matter content is a…
The initial data in the polygon approach to (2+1)D gravity coupled to point particles are constrained by the vertex equations and the particle equations. We establish the hyperbolic nature of the vertex equations and derive some…
We solve the Jang equation with respect to asymptotically hyperbolic "hyperboloidal" initial data. The results are applied to give a non-spinor proof of the positive mass theorem in the asymptotically hyperbolic setting. This work focuses…
In this paper we study a Hamiltonian system with a spatially asymmetric potential. We are interested in the effects on the dynamics when the potential becomes symmetric slowly in time. We focus on a highly simplified non-trivial model…