See https://en.wikipedia.org/wiki/BFR_(rocket)#Second_stage_and_...
The stainless steel hull is a viable design (though obviously given how many times it has changed it might not be final).
Scott Manley did a deep dive: https://www.youtube.com/watch?v=XVgEKBwE2RM
See https://en.wikipedia.org/wiki/BFR_(rocket)#Second_stage_and_...