Physicist Lee Smolin suggests that we can understand the physics at the birth of a new universe via a black hole in the same way that that we understand biological evolution: the "child" universe will contain the same "DNA" of the parents, with very small variations. For this reason, he believes it likely that the universes birthed from emergent black holes are likely to have all or most of the characteristics of their parent universe. The speed of light, for example, is likely to be the same or practically the same. Of course, 100's of billions of black holes will inevitably give birth to a wide variety of "genetically" closely related but unique universes, so over generations each subsequent universe will become more distinct from the parent that birthed it, and from its grandparent universe, great-grandparent universe, etc. that came before it.

Disclaimer: I am no physicist, so my understanding is open to correction by more knowledgable people. If I am wrong about Smolin's interpretation, let me know. :)