Here, we consider a gravity theory involving a spontaneous Lorentz symmetry breaking called the bumblebee model. We show that, at certain values of the bumblebee field, the Gödel metric is consistent within this theory. *
The bumblebee field coupled with gravity is considered. This gravitational theory exhibits spontaneous breaking of Lorentz symmetry. The Gödel-type universe is introduced and then the causality and its violation are studied. Causal and non-causal Gödel-type solutions are obtained for different content of matter.In addition, when the coupling constant, which controls the interaction between the bumblebee field and the gravitational field, is zero the bumblebee potential may be associated with the value of the cosmological constant of the general relativity. Furthermore, the case with the non-zero coupling constant is also investigated.
The Ricci dark energy is a model inspired by the holographic dark energy models with the dark energy density being proportional to Ricci scalar curvature. Here this model is studied in the bumblebee gravity theory. It is a gravitational theory that exhibit spontaneous Lorentz symmetry breaking. Then the modified Friedmann equation is solved for two cases. In the first case the coupling constant ξ is equal to zero. And in the second case a solution in the vacuum, where the bumblebee field becomes a constant that minimizes the potential, is considered. The coupling constant controls the interaction gravity-bumblebee.
In this paper the causality issues are discussed in a non-Riemannian geometry, called Lyra geometry. It is a non-Riemannian geometry originated from Weyl geometry. In order to compare this geometry with the Riemannian geometry, the Einstein field equations are considered. It is verified that the Gödel and Gödeltype metric are consistent with this non-Riemannian geometry. A non-trivial solution for Gödel universe in the absence of matter sources is determined without analogue in general relativity. Different sources are considered and then different conditions for causal and non-causal solutions are discussed.
Here, we consider a gravity theory involving a spontaneous Lorentz symmetry breaking called the bumblebee model. We show that, at certain values of the bumblebee field, the Gödel metric is consistent within this theory.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.