  We generalize the notion of Einstein-Rosen bridge by defining it as a
space-like connection between two universes with regions of asymptotically
minkowskian space-time infinities. The corresponding symmetry and asymmetry
properties of the generalized Einstein-Rosen bridge are considered at the cases
of Reissner-Nordstr\"om and Kerr metrics. We elucidate the versatility of
intriguing symmetry and asymmetry phenomena outside and inside black holes. For
description of the test particle (planet and photon) motion it is used the
Kerr-Newman metric of the rotating and electrically charged black hole. In
particular, it is demonstrated the symmetry and asymmetry of the one-way
Einstein-Rosen bridge inside black hole toward and through the plethora of
endless and infinite universes.
