Causality violations are typically seen as unrealistic and undesirable features of a physical model. The following points out three reasons why causality violations, which Bonnor and Steadman identified even in solutions to the Einstein equation referring to ordinary laboratory situations, are not necessarily undesirable. First, a space-time in which every causal curve can be extended into a closed causal curve is singularity free—a necessary property of a globally applicable physical theory. Second, a causality-violating space-time exhibits a nontrivial topology—no closed timelike curve (CTC) can be homotopic among CTCs to a point, or that point would not be causally well behaved—and nontrivial topology has been explored as a model of particles. Finally, if every causal curve in a given space-time passes through an event horizon, a property which can be called “causal censorship”, then that space-time with event horizons excised would still be causally well behaved.
General relativity Differential geometry Spacetime topology
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