The phrase "central core" refers to the main or most important part of something. It is like the heart or center that everything else revolves around. Full definition
This basic decision, if we can call it that, defines the most central core of a human being. (religion-online.org)
The last station is designed to stress you when you're at your weakest by doing central core movements when you are exhausted from doing the previous 4 stations. (anabolicsmall.com)
To balance their speeds out to those distances from their massive central cores, the galaxies must be made of more stuff than just that which we can detect. (public.nrao.edu)