arXiv subjects
Publications and source records attributed to Tim-Torben Paetz.
As complement to Class. Quantum Grav. 30 (2013) 235036 we analyze Killing initial data on characteristic Cauchy surfaces in conformally rescaled vacuum spacetimes 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.
We prove existence of vacuum space-times with freely prescribable cone-smooth initial data on past null infinity.
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.
We review the basic setup of Kaluza-Klein theory, namely a 5-dimensional vacuum with a cyclic isometry, which corresponds to Einstein-Maxwell-dilaton theory in 4-dimensional spacetime. We first recall the behaviour of Killing horizons and its generators under bundle lift and projection. We then show that the property of compact surfaces of being (stably) marginally trapped is preserved under lift and projection provided the appropriate ("Pauli-") conformal scaling is used for the spacetime metric. We also discuss and compare recently proven area inequalities for stable axially symmetric 2-dimensional and 3-dimensional marginally outer trapped surfaces.
We review various aspects of the characteristic initial value problem for the Einstein equations, presenting new approaches to some of the issues arising.