arXiv subjects
Publications and source records attributed to A. Dirmeier.
For a complete Riemannian metric, a pointwise conformal transformation may lead to a complete or incomplete transformed Riemannian metric, depending on the behavior of the conformal factor. We establish conditions on the growth of the conformal factor towards the infinity of the Riemannian metric, such that the conformally transformed Riemannian metric remains complete.
In 1993 A. Ori \cite{Ori93} presented spacetimes violating the chronology condition in order to answer the question whether a time machine construction has to violate the weak energy condition or not. Later, in 2005 \cite{Ori05}, he constructed a class of time machine solutions with compact vacuum core. Both classes include an interesting global structure and it is possible to obtain closed timelike curves. Besides we focus on the geometric structure, in particular symmetries and geodesics, if feasible, and visualize several aspects.