What is the eventual state of a star after the planetary nebula phase ends and the white dwarf cools?

Answer

A black dwarf, which is a cold, dark, inert remnant

Once the gaseous shell of a planetary nebula has dissipated into space, only the white dwarf remains. Having ceased all nuclear fusion processes, the white dwarf is no longer capable of generating new energy. Over a period spanning billions of years, it gradually radiates away its stored heat. Ultimately, it reaches a state where it is cold, dark, and inert, known as a black dwarf, marking the final stage of its evolution.

What is the eventual state of a star after the planetary nebula phase ends and the white dwarf cools?
astronomystarplanetnebulawhite dwarf