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arXiv · 2407.04750

G\"odel-type spacetimes in $f(Q)$ gravity

A. M. Silva·M. J. Rebouças·N. A. Lemos
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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 G\"odel-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 G\"odel-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 G\"odel-type metrics only G\"odel'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 $f(Q)$.

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BibTeXRIS

A. M. Silva, M. J. Rebouças, N. A. Lemos. 2024-07-04. G\"odel-type spacetimes in $f(Q)$ gravity. https://arxiv.org/abs/2407.04750

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