G\"{o}del-type universes in bumblebee gravity

Understand

The bumblebee field coupled with gravity is considered.

• This gravitational theory exhibits spontaneous breaking of Lorentz symmetry.
• The G\"{o}del-type universe is introduced and then the causality and its violation are studied.
• Causal and non-causal G\"{o}del-type solutions are obtained for different content of matter.