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When a star becomes a white dwarf, it enters a new stage where it no longer has nuclear reactions occurring in its core. This is because it has exhausted all of its nuclear fuel. What's left is a hot, dense core that starts a journey of cooling.
During the cooling process, the white dwarf shines brightly due to the heat leftover from its previous nuclear reactions. However, without new fuel to burn, it gradually loses energy. The loss of heat is a slow process, occurring as the white dwarf radiates its residual energy into the vastness of space. This radiation is in the form of light and other electromagnetic waves, causing the white dwarf to slowly fade over time.
The temperature of a white dwarf decreases gradually, meaning it cools and dims over billions of years. The rate of cooling depends on its mass and composition, but generally, this process is incredibly slow.

The cooling of a white dwarf eventually leads to the theoretical formation of a black dwarf. As the white dwarf radiates away its heat, it gets cooler and darker. Over billions, perhaps even trillions of years, it loses all significant heat and becomes what astronomers call a black dwarf.
A black dwarf is essentially a white dwarf that has cooled to the point where it no longer emits significant heat or light. It's like a shadow of its former self, cold and dark, almost invisible against the backdrop of space.
However, it is important to note that black dwarfs are purely theoretical at this stage. The universe is about 13.8 billion years old, which isn't enough time for any black dwarfs to have formed yet. Therefore, none have been observed.

The path to becoming a white dwarf begins long before the star sheds its outer layers. This journey starts when a star exhausts its nuclear fuel, primarily hydrogen, which it fuses into helium during most of its active lifetime. As the hydrogen fuel depletes, the star begins to burn the helium through a process known as helium fusion.
Once both hydrogen and helium are exhausted, the star can no longer sustain the nuclear reactions that once provided its energy. This exhaustion leads to the collapse of the star's core under its gravity, as the outward pressure from fusion reactions has diminished. What remains is the hot, dense core known as a white dwarf.
This transition marks the end of nuclear fusion and the beginning of the cooling stage. Nuclear fuel exhaustion is a crucial step in the star's lifecycle, setting the stage for its transformation into a white dwarf, and eventually, over time, a black dwarf.