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Discover LudwigThe phrase "inner core" is correct and usable in written English.
You can use it to refer to the deepest layer of a planet or star, or to describe a person's most intimate beliefs or feelings. For example, "He had a strong belief in justice, which he felt came from his inner core."
Dictionary
inner core
noun
The solid material found in the centre of some planets at extremely high temperature and pressure, distinct from the liquid outer core. The innermost part of the Earth, believed to be made of a nickel-iron alloy.
Exact(58)
We fell into that horrible inner core.
The inner core is technical excellence.
Another claims "titanium inner core".
We have a good inner core of guys.
But defining the inner core will be difficult.
This is the novel's inner core, its painful essence.
Armour-piercing bullets have a hardened-steel inner core.
Impact-resistant windows have double-paned glass with an inner core that serves as a buffer.
The underlying difference is the arrangement of electrons in the inner core of the iron ions.
That's what the inner core of her party will think of.
The bottom line is, change now permeates the Giants' inner core.
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com