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Gödel-type metrics in Einstein-Aether theory II: nonflat background in arbitrary dimensions

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Abstract

It was previously proved that the Gödel-type metrics with flat three-dimensional background metric solve exactly the field equations of the Einstein-Aether theory in four dimensions. We generalize this result by showing that the stationary Gödel-type metrics with nonflat background in D dimensions solve exactly the field equations of the Einstein-Aether theory. The reduced field equations are the \((D-1)\)-dimensional Euclidean Ricci-flat and the \((D-1)\)-dimensional source-free Maxwell equations, and the parameters of the theory are left free except \(c_{1}-c_{3}=1\). We give a method to produce exact solutions of the Einstein-Aether theory from the Gödel-type metrics in D dimensions. By using this method, we present explicit exact solutions to the theory by considering the particular cases: (\(D-1\))-dimensional Euclidean flat, conformally flat, and Tangherlini backgrounds.

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Notes

  1. These scalings were initially intended to get rid of the constraint \(c_1-c_3=1\) and also have solutions with nonzero cosmological constant. However, at the end, it turned out that this is not possible (see Proposition 5 below).

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Acknowledgments

We thank the referee for carefully reading our manuscript and providing constructive comments. This work is partially supported by the Scientific and Technological Research Council of Turkey (TUBITAK).

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Authors and Affiliations

  1. Department of Mathematics, Faculty of Sciences, Bilkent University, 06800, Ankara, Turkey

    Metin Gürses

  2. Department of Physics, Faculty of Sciences, Bilkent University, 06800, Ankara, Turkey

    Metin Gürses & Çetin Şentürk

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  1. Metin Gürses
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  2. Çetin Şentürk
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Correspondence to Çetin Şentürk.

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Gürses, M., Şentürk, Ç. Gödel-type metrics in Einstein-Aether theory II: nonflat background in arbitrary dimensions. Gen Relativ Gravit 48, 63 (2016). https://doi.org/10.1007/s10714-016-2058-x

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