Unwrapping Closed Timelike Curves

Closed timelike curves (CTCs) appear in many solutions of the Einstein equation, even with reasonable matter sources. These solutions appear to violate causality and so are considered problematic. Since CTCs reflect the global properties of a spacetime, one can attempt to change its topology, without changing its geometry, in such a way that the former CTCs are no longer closed in the new spacetime. This procedure is informally known as unwrapping. However, changes in global identifications tend to lead to local effects, and unwrapping is no exception, as it introduces a special kind of singularity, called quasi-regular. This "unwrapping" singularity is similar to the string singularities. We give two examples of unwrapping of essentially 2+1 dimensional spacetimes with CTCs, the Gott spacetime and the Godel universe. We show that the unwrapped Gott spacetime, while singular, is at least devoid of CTCs. In contrast, the unwrapped Godel spacetime still contains CTCs through every point. A "multiple unwrapping" procedure is devised to remove the remaining circular CTCs. We conclude that, based on the two spacetimes we investigated, CTCs appearing in the solutions of the Einstein equation are not simply a mathematical artifact of coordinate identifications, but are indeed a necessary consequence of General Relativity, provided only that we demand these solutions do not possess naked quasi-regular singularities.Comment: 29 pages, 9 figure

Dimensional reduction and spacetime pathologies

Dimensional reduction is a well known technique in general relativity. It has been used to resolve certain singularities, to generate new solutions, and to reduce the computational complexity of numerical evolution. These advantages, however, often prove costly, as the reduced spacetime may have various pathologies, such as singularities, poor asymptotics, negative energy, and even superluminal matter flows. The first two parts of this thesis investigate when and how these pathologies arise. After considering several simple examples, we first prove, using perturbative techniques, that under certain reasonable assumptions any asymptotically flat reduction of an asymptotically flat spacetime results in negative energy seen by timelike observers. The next part describes the topological rigidity theorem and its consequences for certain reductions to three dimensions, confirming and generalizing the results of the perturbative approach. The last part of the thesis is an investigation of the claim that closed timelike curves generically appearing in general relativity are a mathematical artifact of periodic coordinate identifications, using, in part, the dimensional reduction techniques. We show that removing these periodic identifications results in naked quasi-regular singularities and is not even guaranteed to get rid of the closed timelike curves.Science, Faculty ofPhysics and Astronomy, Department ofGraduat

Line profiles of accretion disks around black holes in Schwarzschild-de Sitter and Einstein-Yang-Mills spacetimes

We investigate the characteristic peaks in the iron line profile in the black hole accretion disk X-ray spectrum in two static spherically symmetric metrics, Schwarzschild-de Sitter metric and the Einstein-Yang-Mills black hole metric. For the Schwarzschild-de Sitter metric our results show that for a fixed mass black hole, the peaks become less pronounced and closer together with increasing cosmological constant A. This effect is mainly due to the slower rotational velocity of Keplerian orbits at large radii in the Schwarzschild-de Sitter spacetime as compared to that for the Schwarzschild spacetime. This change of the iron line profile is similar to that obtained from extending the accretion disk size or reducing the emission power law exponent in the Schwarzschild black hole accretion disk models. Based upon the current estimates of A, black holes of at least 1018 solar masses are required to make the effect observable. For Einstein-Yang-Mills black holes, the line profiles depend strongly on the horizon radius and the solution number n. For n = 1 the profile is similar to that of a Schwarzschild black hole. In contrast, the shallow slope of the g00 component of the metric for n = 2,3,4 solutions increases the line width for these solutions significantly, in some cases creating a second pair of peaks redshifted approximately by a factor of 2, breaking the usual correspondence between the position of the blue peak and the black hole mass. The line profiles of solutions for n = 5 — 8 and higher, depending on the horizon radius, closely resemble that of extreme Reissner-Nordstrom black hole. In addition, due to an island of orbit stability near the Einstein-Yang-Mills black-hole horizon for the solutions with small horizon radius r/, there is an extra pair of peaks in the line profile redshifted by a factor of 30 times or more relative to the main line. These features might be used to distinguish accreting Einstein-Yang-Mills black holes from Schwarzschild and Kerr black holes.Science, Faculty ofPhysics and Astronomy, Department ofGraduat