Regular phantom black holes

For self-gravitating, static, spherically symmetric, minimally coupled scalar fields with arbitrary potentials and negative kinetic energy (favored by the cosmological observations), we give a classification of possible regular solutions to the field equations with flat, de Sitter and AdS asymptotic behavior. Among the 16 presented classes of regular rsolutions are traversable wormholes, Kantowski-Sachs (KS) cosmologies beginning and ending with de Sitter stages, and asymptotically flat black holes (BHs). The Penrose diagram of a regular BH is Schwarzschild-like, but the singularity at $r=0$ is replaced by a de Sitter infinity, which gives a hypothetic BH explorer a chance to survive. Such solutions also lead to the idea that our Universe could be created from a phantom-dominated collapse in another universe, with KS expansion and isotropization after crossing the horizon. Explicit examples of regular solutions are built and discussed. Possible generalizations include $k$-essence type scalar fields (with a potential) and scalar-tensor theories of gravity.