Other
Scientific paper
Dec 1994
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1994phrvd..50.7244h&link_type=abstract
Physical Review D (Particles, Fields, Gravitation, and Cosmology), Volume 50, Issue 12, 15 December 1994, pp.7244-7259
Other
18
Spacetime Topology, Causal Structure, Spinor Structure, Exact Solutions
Scientific paper
We investigate the global geometries of (2+1)-dimensional spacetimes as characterized by the transformations undergone by tangent spaces upon parallel transport around closed curves. We critically discuss the use of the term ``total energy-momentum'' as a label for such parallel-transport transformations, pointing out several problems with it. We then investigate parallel-transport transformations in the known (2+1)-dimensional spacetimes containing closed timelike curves (CTC's), and introduce a few new such spacetimes. Using the more specific concept of the holonomy of a closed curve, applicable in simply connected spacetimes, we emphasize that Gott's two-particle CTC-containing spacetime does not have a tachyonic geometry. Finally, we prove the following modified version of Kabat's conjecture: if a CTC is deformable to spacelike or null infinity while remaining a CTC, then its parallel-transport transformation cannot be a rotation; therefore its holonomy, if defined, cannot be a rotation other than through a multiple of 2π.
Gott Richard J. III
Headrick Matthew P.
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