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Lagrangian formalism for Rastall theory of gravity and Gödel-type universe

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Abstract

In the Rastall gravity a non-minimal coupling between geometry and matter fields is considered. Then the usual energy-momentum tensor conservation law is not valid. Here a Lagrangian formalism is proposed to the Rastall theory of gravity. The Gödel-type universe is studied in this gravitational model. Then it is studied whether this theory permits causality violation. The field equations do not exclude solutions with a breakdown of causality for a perfect fluid as matter content. In this case, an expression for the critical radius (beyond which the causality is violated) is determined. In addition, for a combination between perfect fluid and scalar field as matter content the theory accommodates causal Gödel-type solution.

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Acknowledgements

This work by A. F. S. is supported by CNPq projects 308611/2017-9 and 430194/2018-8; W. A. G. M. thanks CAPES for financial support.

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Correspondence to A. F. Santos.

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De Moraes, W.A.G., Santos, A.F. Lagrangian formalism for Rastall theory of gravity and Gödel-type universe. Gen Relativ Gravit 51, 167 (2019). https://doi.org/10.1007/s10714-019-2652-9

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Keywords

  • Lagrangian formalism
  • Rastall theory
  • Gödel-type universe
  • Causality violation