Related papers: Type D conformal initial data
We prove the existence of a family of initial data for the Einstein vacuum equation which can be interpreted as the data for two Kerr-like black holes in arbitrary location and with spin in arbitrary direction. When the mass parameter of…
In d+1 dimensions we solve the equations of motion for the case of gravity minimally or conformally coupled to a scalar field. For the minimally coupled system the equations can either be solved directly or by transforming vacuum solutions,…
We apply a new method with explicit solution operators to construct asymptotically flat initial data sets of the vacuum Einstein equation with new localization properties. Applications include an improvement of the decay rate in…
We consider the conformal wave equation on the Einstein cylinder with a defocusing cubic non-linearity. Motivated by a method developed by Rostworowski-Maliborski on the existence of time periodic solutions to the spherically symmetric…
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 consider the Einstein-Maxwell equations in space-dimension $n$. We point out that the Lindblad-Rodnianski stability proof applies to those equations whatever the space-dimension $n\ge 3$. In even space-time dimension $n+1\ge 6$ we use…
Motivated by recent accelerating cosmological model, we derive the solutions to vacuum Einstein equation in $(d+1)$-dimensional Minkowski space with $n$-dimensional hyperbolic manifold. The conditions of accelerating expansion are given in…
In this paper we continue earlier investigations of evolutionary formulations of the Einstein vacuum constraint equations originally introduced by R\'{a}cz. Motivated by the strong evidence from these works that the resulting vacuum initial…
The Petrov type I condition for the solutions of vacuum Einstein equations in both of the non-relativistic and relativistic hydrodynamic expansions is checked. We show that it holds up to the third order of the non-relativistic hydrodynamic…
We study formal expansions of asymptotically flat solutions to the static vacuum field equations which are determined by minimal sets of freely specifyable data referred to as `null data'. These are given by sequences of symmetric trace…
The construction of the cylinder at spatial infinity for stationary spacetimes is considered. Using a specific conformal gauge and frame, it is shown that the tensorial fields associated to the conformal Einstein field equations admit…
This is the third paper in a series describing a numerical implementation of the conformal Einstein equation. This paper describes a scheme to calculate (three) dimensional data for the conformal field equations from a set of free…
We show that to every small and decaying solution of the linearized constraint equations about Minkowski spacetime, one can add a quadratically small correction to obtain a solution of the full constraint equations. Near spacelike infinity,…
By suitably re-scaling the conformal Einstein's equations we are able to apply recent results in the theory of PDE, and prove that they possess slow solutions in a future neighborhood of an initial surface reaching ${\cal I}^+$. The…
In principle, global properties of solution of Einstein equations need to be addressed using the conformal Einstein equations, because this conformal compactification allows a clean definition of the `infinities' (spacelike, timelike and…
It is well-known that small, regular, spherically symmetric characteristic initial data to the Einstein-scalar-field system which are decaying towards (future null) infinity give rise to solutions which are foward-in-time global (in the…
We make use of Friedrich's construction of the cylinder at spatial infinity to relate the logarithmic terms appearing in asymptotic expansions of components of the Weyl tensor to the freely specifiable parts of time symmetric initial data…
This is the second in a series of articles on the numerical solution of Friedrich's conformal field equations for Einstein's theory of gravity. We will discuss in this paper the numerical methods used to solve the system of evolution…
We analyze the Cauchy problem for the vacuum Einstein equations with data on a complete light-cone in an asymptotically Minkowskian space-time. We provide conditions on the free initial data which guarantee existence of global solutions of…
In this paper we have applied the generalized Kerr-Schild transformation finding a new family of stationary perfect-fluid solutions of the Einstein field equations. The procedure used combines some well-known techniques of null and timelike…