Recurrence Metrics and Time Varying Light Cones

TL;DR

This paper constructs new metrics in General Relativity where light cones flip periodically, enabling solutions that exhibit recurrence and velocity reversions, extending previous no-go theorems to new spacetime geometries.

Contribution

It introduces novel metrics with periodic light cone flips, demonstrating recurrence in General Relativity beyond expanding universe models.

Findings

Light cones flip periodically between past and future.

Geodesics show periodic velocity reversions.

Matter tensors exhibit unusual periodic variations.

Abstract

It is shown by explicit construction of new metrics, that General Relativity can solve the exact Poinc$\acute{a}$re recurrence problem. In these solutions, the light cone, flips periodically between past and future, due to a periodically alternating arrow of the proper time. The geodesics in these universes show periodic Loschmidt's velocity reversion $v \to -v$, at critical points, which leads to recurrence. However, the matter tensors of some of these solutions exhibit unusual properties - such as, periodic variations in density and pressure. While this is to be expected in periodic models, the physical basis for such a variation is not clear. Present paper therefore can be regarded as an extension of Tipler's "no go theorem for recurrence in an expanding universe", to other space-time geometries.