Not saying I understand GR's spacetime curvature to a great degree, but what I do 'know', it does not require a forth space dimension to 'bend' into. In other words, all curvature is intrinsic to our normal three spatial plus time dimensions. The following is from the book ''The Science of Interstellar'' by Kip Thorne The film made great play of its graphical representation of a black hole. To me, the book seems to mislead with this ''warped in a higher -dimensional bulk.'' Yes, I know it pop-science, but it's the first time I've come across the use of the bulk to explain GR. Please Register or Log in to view the hidden image!