Multiply connected spacetimes and closed timelike curves in semiclassical gravity

Citation

Klinkhammer, Gunnar Ulrich (1992) Multiply connected spacetimes and closed timelike curves in semiclassical gravity. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/694e-b162. https://resolver.caltech.edu/CaltechTHESIS:08302011-113709010

Abstract

In this thesis, we present three studies motivated by the recent interest in spacetimes with closed timelike curves ("CTC's"). First, it has been shown that certain energy conditions must be violated if spacetime is to develop CTC's. We initiate a study of whether quantum field theory permits such violations by proving that, in Minkowski spacetime, a free scalar field will satisfy the weak and strong energy conditions averaged along any complete null or timelike geodesic. We remark that in fiat, but topologically nontrivial spacetimes, the averaged weak energy condition can be violated. Second, it has been argued that the most likely way by which Nature might prevent the creation of CTC's is a divergent vacuum polarization at the chronology horizon where such CTC's first arise. We derive the form of the vacuum polarization of a conformal scalar field and of a spin-1/2 field near a closed null geodesic from which the null generators of a generic compactly generated chronology horizon spring forth. We show that the tensorial structure of the polarization and its degree of divergence are the same for scalar and for spin-1/2 fields and are independent of the details of the spacetime geometry. We also show that in generic cases, there will be no cancellation of this divergence for a combination of scalar and spin-1/2 fields that has equal numbers of Fermi and Bose degrees of freedom. Third, in anticipation of the possibility that Nature might permit CTC's, we demonstrate that for a classical body with a hard-sphere potential and no internal degrees of freedom (a "billiard ball") traveling nonrelativistically in a wormhole spacetime with CTC's, the Cauchy problem is ill-posed in a peculiar way. For certain ("dangerous") initial data, there would appear to be no self-consistent solution to the equations of motion because the ball collides with its younger self after having traversed the wormhole. However, we show that for a wide range of dangerous and non-dangerous initial data, there is an infinity of self-consistent solutions, each involving one self-collision. No initial data are found for which there is no self-consistent solution.

Thesis Files