Gödel-type spacetimes in $f(Q)$ gravity

Abstract

There is ongoing interest in the nonmetricity formulation of gravity. The nonlinear extension of the theory, called $f(Q)$ gravity, has recently been proposed and offers a promising avenue for addressing some of the long-standing challenges in cosmology and fundamental physics. A number of solutions have already been found that have confirmed the usefulness of the theory for astrophysics and cosmology. Motivated by earlier work on Gödel-type spacetimes we investigate whether $f(Q)$ gravity admits such cosmological solutions, which entail causality violation. In the coincident gauge, which is shown to be a legitimate gauge because the connection field equations are satisfied, we find that Gödel-type metrics are allowed by this modified gravity theory for any function $f(Q)$. Noncausal and causal solutions exist depending on the matter content. For a perfect fluid, out of all Gödel-type metrics only Gödel's original model is allowed in $f(Q)$ gravity, implying violation of causality. The requirement that energy conditions be obeyed by the fluid leads to mild restrictions on $f(Q)$. For a massless scalar field in the presence of a cosmological constant, there are causal solutions for any reasonable function $f(Q)$.

Title changed; substantially enlarged; noncausal and causal solutions shown to exist; 19 pages; accepted by the Int. J. Mod. Phys. D