Timelike infinity and asymptotic symmetry

Timelike Infinity and Asymptotic Symmetry

By extending Ashtekar and Romano’s definition of spacelike infinity to the timelike direction, a new definition of asymptotic flatness at timelike infinity for an isolated system with a source is proposed. The treatment provides unit spacelike 3-hyperboloid timelike infinity and avoids the introduction of the troublesome differentiability conditions which were necessary in the previous works on...

From Now to Timelike Infinity on a Finite Grid

In the articles [1, 2, 3, 4] we presented a complete code for solving the conformal Einstein equations which will allow us to study many interesting questions about the global structure of spacetimes by performing numerical experiments. In the present paper we want to demonstrate some of the unique capabilities of this code by a simple example: We calculate the time evolution of gravitational w...

Justification of an asymptotic expansion at infinity

A family of asymptotic solutions at infinity for the system of ordinary differential equations is considered. Existence of exact solutions which have these asymptotics is proved.

On the Injectivity and Asymptotic Stability at Infinity

Let X : U → R be a differentiable vector field defined on the complement of a compact subset of the plane. Let Spc(X) denote the set of all eigenvalues of the differential DXz , when z varies in whole the domain U. We prove that the condition Spc(X) ⊂ {z ∈ C : R(z) < 0} is enough in order to obtain that the infinity to be either an attractor or a repellor for X. More precisely, we show that (i)...

Semilinear Elliptic Equations Having Asymptotic Limits at Zero and Infinity