Our best educated guess is that singularity consists of a randomly connected four-dimensional space (no time) called quantum foam.

We don’t know enough about quantum gravity to understand the properties of this “foam” in much detail, but:

• An infinite variety of “foam” configurations are possible; a particle falling into a singularity has a certain non-zero probability of finding each possible configuration.
• The next infalling particle would most likely find it (or cause it to be in) in a different configuration.
• Since time doesn’t exist in the foam, there is no natural tendency for this “time origin” to connect in any predetermined way to spacetime outside the mass-density singularity.

Some of the foam configurations might in fact connect better to surrounding spacetime in which expansion takes place, as in the Big Bang, rather than the contraction characteristic of black-hole formation.

Another way to look at this is that in expanding mode, time flows out of the mass-density singularity (like in the real Big Bang), rather than in (like in black hole formation).

Thus it seems as though the singularity might switch back and forth between collapsing and expanding modes as it interacts with other masses and energies in the black hole’s interior.  Implications:

• As it switches states, the singularity pushes and pulls the spacetime within the black hole’s horizon.
• “Baby universes” may form inside massive black holes. (This is the basis of many a science-fiction story...)

Black holes with their singularities in expanding configuration provide a useful paradigm for the formation of wormhole : a connection through hyperspace (space with more than 3 dimensions) of two regions in spacetime that contain such singularities.