TL;DR
This paper introduces a general definition for the boundaries of the chronology violating region in spacetime, extending previous work by not requiring the complement to be globally hyperbolic, and explores related singularity theorems.
Contribution
It provides a new, more general definition for the boundary of the chronology violating set and proves properties like compact generation of horizons without assuming global hyperbolicity.
Findings
Proposed a general boundary definition for chronology violating regions
Proved that compactly generated horizons are compactly constructed
Confirmed the reasonability of the new boundary definition through propositions
Abstract
A sufficiently general definition for the future and past boundaries of the chronology violating region is given. In comparison to previous studies, this work does not assume that the complement of the chronology violating set is globally hyperbolic. The boundary of the chronology violating set is studied and several propositions are obtained which confirm the reasonability of the definition. Some singularity theorems related to chronology violation are considered. Among the other results we prove that compactly generated horizons are compactly constructed.
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