Tim-Torben Paetz

The many ways of the characteristic Cauchy problem

We review various aspects of the characteristic initial-value problem for the Einstein equations, presenting new approaches to some of the issues arising.

Solutions of the vacuum Einstein equations with initial data on past null infinity

We prove existence of vacuum space-times with freely prescribable cone-smooth initial data on past null infinity.

Characteristic initial data and smoothness of Scri. II. Asymptotic expansions and construction of conformally smooth data sets

We derive necessary-and-sufficient conditions on characteristic initial data for Friedrichs conformal field equations in 3 + 1 dimensions to have no logarithmic terms in an asymptotic expansion at null infinity.

The mass of light-cones

We give an elementary proof of positivity of total gravitational energy in space-times containing complete smooth light-cones.

Algorithmic characterization results for the Kerr-NUT-(A)dS space-time. I. A space-time approach

We provide an algorithm to check whether a given vacuum space-time (M,g) admits a Killing vector field with respect to which the Mars-Simon tensor vanishes. In particular, we obtain an algorithmic procedure to check whether (M,g) is locally isometric to a member of the Kerr-NUT-(A)dS family. A particular emphasis will be devoted to the Kerr-(A)dS case.

KIDs prefer special cones

As complement to Chru?ciel and Paetz (2013 Class. Quantum Grav. 30 235036) we analyse Killing Initial Data (KID) on characteristic Cauchy surfaces in conformally rescaled vacuum space-times satisfying Friedrich?s conformal field equations. As an application, we derive and discuss the KID equations on a light-cone with vertex at past timelike infinity.

KIDs like cones

We analyze vacuum Killing Initial Data on characteristic Cauchy surfaces. A general theorem on existence of Killing vectors in the domain of dependence is proved, and some special cases are analyzed in detail, including the case of bifurcate Killing horizons.

On the smoothness of the critical sets of the cylinder at spatial infinity in vacuum spacetimes

We analyze the appearance of logarithmic terms at the critical sets of Friedrichs cylinder representation of spatial infinity. It is shown that if the radiation field vanishes at all orders at the critical sets no logarithmic terms are produced in the formal expansions. Conversely, it is proved that, under the additional hypothesis that the spacetime has constant (ADM) mass aspect and vanishing dual (ADM) mass aspect, this condition is also necessary for a spacetime to admit a smooth representation at the critical sets.

Analysis of a Bianchi-like equation satisfied by the Mars-Simon tensor

The Mars-Simon tensor (MST), which e.g. plays a crucial role to provide gauge invariant characterizations of the Kerr-NUT-(A)(dS) family, satisfies a Bianchi-like equation. In this paper we analyze this equation in close analogy to the Bianchi equation, in particular it will be shown that the constraints are preserved supposing that a generalized Buchdahl condition holds. This permits the systematic construction of solutions to this equation in terms of a well-posed Cauchy problem. A particular emphasis lies on the asymptotic Cauchy problem, where data are prescribed on a spacelike scri (i.e. for

Multiple Killing horizons

\Lambda >0