Abstract
Gödel universe, one of the most interesting exact solutions predicted by General Relativity, describes a homogeneous rotating universe containing naked closed time-like curves (CTCs). It was shown that such CTCs are the consequence of the null energy condition in General Relativity. In this paper, we show that the Gödel-type metrics with chronology protection can emerge in Einstein–Horndeski gravity. We construct such exact solutions also in Einstein–Horndeski–Maxwell and Einstein–Horndeski–Proca theories.
Highlights
Godel metric [1], constructed in 1949, is one of the most interesting exact solutions predicted by General Relativity (GR)
In the previous related works [21], we found within the framework of Einstein gravity, the null energy condition requires that α ≤ 1, and the Godel metrics in Einstein gravity necessary have naked closed time-like curves (CTCs)
We considered a class of Godel metrics (2.1) with a free parameter α
Summary
Godel metric [1], constructed in 1949, is one of the most interesting exact solutions predicted by General Relativity (GR). Naked CTCs are unavoidable for Godel metrics in Einstein gravity, unless α = 1, which corresponds to a direct product of a real line and anti-de Sitter spacetime (AdS) in three dimensions. In the low-energy effective theory of strings with higher-derivative corrections, Godel metrics with α > 1 was constructed in [7]. It is of interest to look for ghost-free theories beyond Einstein gravity that support Godel metrics with α > 1 so that the spacetime is absent from CTCs. In this paper, we construct Godel metrics in Einstein-Horndeski gravity. As a modified theory to Einstein gravity, its null energy condition is modified, and Horndeski gravity may restore the chronological protection, and we find that it is the case.
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