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The building of a time machine, if possible at all, requires the relevantregions of spacetime to be compact (that is, physically speaking, free fromsources of unpredictability such as infinities and singularities). Motivated bythis argument we consider the spacetimes with the compactly determined Cauchyhorizons (CDCHs), the defining property of which is the compactness of$\overline{J^-(\EuScript U)}\cap J^+(\EuScript S_0)$, where $\EuScript U$ is anopen subset of the Cauchy horizon and $\EuScript S_0$ is a Cauchy surface ofthe initial globally hyperbolic region $\ingh$. The following two facts areestablished: 1) $\ingh$ has no globally hyperbolic maximal extension. Thismeans that by shaping appropriately a precompact portion of a globallyhyperbolic region one can \emph{force} the Universe to produce either a closedcausal curve, or a quasiregular singularity, whichever it abhors less; 2)Before a CDCH is formed a null geodesic appears which infinitely approaches thehorizon returning again and again in the same --- arbitrarily small --- region.The energy of the photon moving on such a geodesic increases with each passage,or at least falls insufficiently fast. As a result, an observer located in thementioned region would see a bunch of photons passing through his laboratorywith the arbitrarily large total energy. We speculate that this phenomenon mayhave observable consequences.

Time machines with the compactly determined Cauchy horizon