  In 6D general relativity with a phantom scalar field as a source of gravity,
we present solutions that implement a transition from an effective 4D geometry
times small extra dimensions to an effectively 6D space-time where the physical
laws are different from ours. We consider manifolds with the structure M0 x M1
x M2, where M0 is 2D Lorentzian space-time while each of M1 and M2 can be a
2-sphere or a 2-torus. Some solutions describe wormholes with spherical
symmetry in our space-time and toroidal extra dimensions. Others are of black
universe type: at one end there is a 6D asymptotically anti-de Sitter black
hole while beyond the horizon the geometry tends to a 4D de Sitter cosmology
times a small 2D spherical extra space.
