Question

Are there relativistic theories with spacetime modelled on $\mathbb C^4$ rather than real Minkowski space $\mathbb R^4$?

Answer 1

No there and realistic theories with spacetime molded because the theories compared with space time is not equal to the earth's gravity or pull That depends upon the different types of theorems which is been applied.

Answer 2

Does anybody know of references to theories where relativity & spacetime is modelled on a (complex/Kähler) manifold which is locally diffeomorphic to C4 rather than R4, hence on a manifold of real dimension 8 rather than 4. I'm interested in both the classical and quantum case