Recurrence metrics and the physics of closed time-like curves

TL;DR

This paper explores vacuum solutions in Einstein's equations for a universe with circular time topology, analyzing how closed time-like curves affect causality, recurrence, and the universe's physical properties.

Contribution

It introduces a model of a universe with circular time, demonstrating how CTCs can be consistent with causality and exhibit recurrence phenomena.

Findings

Universe with S^1 time topology behaves like a time-machine

Geodesics form closed time-like curves (CTCs)

Universe remains free of causality paradoxes

Abstract

We investigate vacuum solutions of Einstein's equation for a universe with an S^1 topology of time. Such a universe behaves like a time-machine and has geodesics which coincide with closed time-like curves (CTCs). A system evolving along a CTC experiences the Loschmidt velocity reversion and undergoes a recurrence commensurate with the universal period. We indicate why this universe is free of the causality paradoxes, usually associated with CTCs.