Closed timelike loops in homogeneous rotating $$\varLambda $$ Λ -dust cosmologies

Abstract

We analyze what we believe to be all known homogeneous rotating \(\varLambda \)-dust cosmologies, to see if they contain closed timelike loops (CTLs). We investigate only these exact GR solutions because they appear to most closely resemble our own universe (apart from rotation and expansion). These solutions are all somewhat similar to the Godel solution, which is known to contain CTLs. Of these solutions, it turns out that exactly those with \(\varLambda <0\) possess CTLs. The paper also analyzes the solutions to see if they satisfy the four “Energy Conditions” (Weak, Null, Strong, Dominant), and shows that all four are satisfied—but only by the families containing CTLs! It is amusing to note that our current universe violates the Strong Energy Condition.