Gravitational Waves from Thurston Geometries

It has been established that the famous three-dimensional Thurston geometries have four intrinsically Lorentzian analogs. We explore these spacetimes in three-dimensional general relativity nonminimally coupled to a scalar field together with electromagnetic matter. We find that three of these spacetimes support electromagnetic radiation, while, the other is partially sourced by a nonnull field and supports gravitational radiation. By addressing this problem we have also found a novel type of gravitational Cheshire effect.