C. Furtado, J. R. Nascimento, A. Yu. Petrov, A. F. Santos
We formulate the nonminimal aether-modified gravity whose action represents itself as a sum of the usual Einstein-Hilbert action and the CPT-even Lorentz-breaking aether-like gravity term proposed by Carroll. For this theory, we show that the G\"{o}del metric solves the modified Einstein equations under a corresponding modification of the matter, while, for the small Lorentz-breaking corrections, the matter turns out to be usual (neither ghost nor phantom one). From the other side, if the matter is suggested to be the same as in the usual general relativity, the G\"{o}del metric must be modified by additive terms proportional to the Lorentz-breaking parameter to achieve its consistency with new equations of motion. Moreover, despite such a modification turns out to be nontrivial and cannot be completely removed via change of variables, nevertheless, the closed timelike curves (CTCs) can exist for a new metric.
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http://arxiv.org/abs/1109.5654
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