Final answer:
Nuclear burning in the center of a star with 15 to 20 times the mass of our Sun stops when it runs out of hydrogen fuel and eventually when the star explodes in a supernova, not when it forms a black hole or reaches the red giant phase.
Step-by-step explanation:
In a star with 15 to 20 times the mass of our Sun, nuclear burning at the center stops when the star runs out of hydrogen fuel, which is the primary source for nuclear fusion. This is the start of a multi-stage process; after the hydrogen is depleted, the core collapses and the star can burn heavier elements like helium, carbon, and so on, eventually leading to the creation of an iron core. When iron fusion begins, it consumes energy instead of releasing it. If the star's iron core becomes too massive (exceeding the Chandrasekhar limit but staying under approximately 3 solar masses), the core will collapse and become incredibly dense, leading to the creation of a neutron star. If the core collapses, this can trigger a supernova explosion, blowing off the outer layers of the star. Thus, nuclear burning in the center of a massive star stops when the star explodes in a supernova, option 4 on the list provided by the student.