Related papers: Unique continuation from infinity in asymptoticall…
In this paper, the following two propositions are proven under the dominant energy condition for the matter field in the higher-dimensional spherically symmetric spacetime in Einstein-Gauss-Bonnet gravity in the presence of a cosmological…
In this short note, we verify explicitly in static coordinates that the non trivial asymptotic Killing vectors at spatial infinity for anti-de Sitter space-times correspond one to one to the conformal Killing vectors of the conformally flat…
The strong unique continuation property for Einstein metrics can be concluded from the well-known fact that Einstein metrics are analytic in geodesic normal coordinates. Here we give a proof of the same result that given two Einstein…
We consider asymptotically anti-de Sitter spacetimes in three-dimensional topologically massive gravity with a negative cosmological constant, for all values of the mass parameter $\mu$ ($\mu\neq0$). We provide consistent boundary…
This paper investigates the decay properties of solutions to the massive linear wave equation $\Box_g \psi + \frac{{\alpha}}{l^2} \psi =0$ for $g$ the metric of a Kerr-AdS spacetime satisfying $|a|l<r_+^2$ and $\alpha<9/4$ satisfying the…
Anti--de Sitter spacetime is important in general relativity and modern field theory. We review its geometrical features and properties of light signals and free particles moving in it. Applying only elementary tools of tensor calculus we…
The conformal structure of the Schwarzschild-de Sitter spacetime is analysed using the extended conformal Einstein field equations. To this end, initial data for an asymptotic initial value problem for the Schwarzschild-de Sitter spacetime…
We present a comprehensive discussion of gravitational charges and radiation in four-dimensional asymptotically locally de Sitter (AldS) spacetimes. Such spacetimes have compact spatial sections and possess spacelike past and future…
This article surveys the research presented by the author at the MATRIX Institute workshop "Hyperbolic Differential Equations in Geometry and Physics" in April 2022. The work is centered about establishing rigorous mathematical statements…
We consider the limit $a\rightarrow \infty$ of the Kerr-de Sitter spacetime. The spacetime is a Petrov type-D solution of the vacuum Einstein field equations with a positive cosmological constant $\Lambda$, vanishing Mars-Simon tensor and…
The behaviour of stationary gravitational perturbations is studied for generalised static black holes in spacetimes of greater than three dimensions, using the formulation developed by the present author and Ishibashi. For the case in which…
We derive the asymptotic solutions for vacuum spacetimes with non-zero cosmological constant $\Lambda$, using the Newman-Penrose formalism. Our approach is based exclusively on the physical spacetime, i.e. we do not explicitly deal with…
We prove that any analytic vacuum spacetime with a positive cosmological constant in four and higher dimensions, that contains a static extremal Killing horizon with a maximally symmetric compact cross-section, must be locally isometric to…
Friedrich's proofs for the global existence results of de Sitter-like space-times and of semi-global existence of Minkowski-like space-times [Comm. Math. Phys. \textbf{107}, 587 (1986)] are re-examined and discussed, making use of the…
In this work, we compute the gravitational wave displacement and spin memory effects in de Sitter spacetime. Gravitational waves in asymptotically flat spacetimes are described by the Bondi-Sachs framework, where radiation at null infinity…
The aim of this manuscript is to review the studies about de Sitter solution and the null infinity of asymptotically flat and de Sitter space-times. Thus, after introducing the de Sitter space-time, the symmetry group is described. Also…
The infinite cosmological "constant" limit of the de Sitter solutions to Einstein's equation is studied. The corresponding spacetime is a singular, four-dimensional cone-space, transitive under proper conformal transformations, which…
We give a new proof of the recent result by Fournodavlos-Schlue on the nonlinear stability of the expanding region of Kerr-de Sitter spacetimes as solutions of the Einstein vacuum equations with positive cosmological constant. Our gauge is…
The asymptotic symmetry group (ASG) at future null infinity (I^+) of four-dimensional de Sitter spacetimes is defined and shown to be given by the group of three-dimensional diffeomorphisms acting on I^+. Finite charges are constructed for…
We prove a unique continuation from infinity theorem for regular waves of the form $[ \Box + \mathcal{V} (t, x) ]\phi=0$. Under the assumption of no incoming and no outgoing radiation on specific halves of past and future null infinities,…