1. Abstract
The theoretical possibility of time travel - in the sense that closed timelike curves (CTCs) occur which
allow a timelike observer to return to some event in his own past - has been studied for quite a while in
the context of general relativity [Nahin]. A series of intriguing results were obtained that proved that
closed timelike curves mathematically do exist. In 1967 the physicist Charles Misner introduced the
Misner space [Misner] as a basic spacetime with CTCs. The more sophisticated causality violating
pseudo-Schwarzschild spacetime was proposed by Amos Ori in 2007 [Ori].
This thesis is organized as follows: We begin with a few preliminaries regarding the relevant basic
concepts of differential geometry which are the foundation for our further research (Chapter 1). In
Chapter 2 we give a brief exposition of causal properties of spacetimes while Chapter 3 is intended to
draw attention to the notion of the 2-dimensional cylindrical spacetime.
The body of this thesis is divided into two parts. The purpose of the first portion is to analyze two
seemingly different spacetimes: The Misner and the pseudo-Schwarzschild spacetimes (Chapters 4-5).
We wish to shed some new light on their pathologies, e.g. the quasiregular singularities and CTCs. It
turns out that these two spacetimes are related regarding their properties from a chronological and
global point of view. According to this result the pseudo-Schwarzschild cylinder can be regarded as a
non-flat generalization of the Misner space. But it also can be obtained from the familiar Schwarzschild
spacetime by Wick rotation. We indicate how Wick rotation may be used to simplify the computation of
the Riemann curvature tensor and to make connections between different spacetimes. In addition,
Chapter 4 is dedicated to the study of geodesic incompleteness in Misner space and in this regard we
construct an analytic non-Hausdorff extension. We also expand the results of the maximal analytic
extension to the Misner covering space. In so doing we obtain the interesting finding that there are two
fundamentally different Misner covering spaces. From this we can conclude that there exist two
versions of Misner space. In Chapters 4-7 the pseudo-Schwarzschild and Misner spacetimes are
inspected in terms of closed timelike curves, geodesics, curvature and their relatedness to each other.
This gives rise to a conjecture which says that Misner space and pseudo-Schwarzschild spacetime are
isocausal.
A further aim of this work is to create a new chronology violating spacetime that describes a
generalization of the precedent ones. We derive the pseudo-Reissner-Nordstrom spacetime from the
well-known Reissner-Nordstrom spacetime and review our main results in this more general setting.
Chapter 8 is devoted to the study of the pseudo-Reissner-Nordstrom spacetime as to its geometrical
structure and causal properties. This diploma thesis concludes with a brief discussion of plausibility
questions and addresses the hierarchy of causality conditions (Chapter 9).