hollow
Each fibre/fiber has a hollow core.

dense, solid, strong
copper, iron, etc.
reactor
nuclear reactor cores

central, essential, inner, innermost, very
This is seen as the central core of the government's policy.
A new spirit welled up from the very core of the nation.

outer
common
a common core of shared understanding

hard
A hard core of supporters gathered to see the star arrive.
hard-core party members

emotional
the emotional core of her music

form, make up
These ideas formed the core of his philosophy.

surround
get to
We want to get to the core of the problem.

at sth's core
At the core of our convictions is belief in individual liberty.

to the core
She was shaken to the core by the news.
He's a politician to the core (= in all his attitudes, beliefs and actions).

the earth's core
heat from the earth's core

Core is used with these nouns as the object:
apple

Core is used with these nouns:
audience, belief, business, collection, competence, component, concept, constituency, curriculum, discipline, element, funding, ideology, message, philosophy, principle, requirement, strength, subject, supporter, technology, worker