Are there causal vacuum solutions with the symmetries of the Gödel universe in higher-derivative gravity?

Abstract

A globally causal vacuum solution with the symmetries of the Gödel universe is obtained in the framework of higher-derivative gravity. This very peculiar and rare result has no similar one in standard general relativity. The Rebouças-Tiomno universe, i.e., the unique completely causal Gödel-type solution of Einsteins field equations with an algebraic Segrè characteristic [(1,11)1], is shown to be a special case of our solution. We also show that our model is an embedding of the three-dimensional antide Sitter universe in four-dimensional space-time. © 1988 The American Physical Society.