The collapse of a star's core under its own gravity is primarily caused by the exhaustion of nuclear fuel in the core, which results in a lack of sufficient energy to counteract the inward pull of gravity. The exact process and outcome depend on the mass of the star.
For stars with masses up to about three times that of the Sun, the collapse of the core leads to a supernova explosion. When nuclear fusion reactions cease in the core, the pressure generated by these reactions is no longer able to counteract gravity. The core rapidly contracts under the force of gravity, causing it to become extremely dense. As the core collapses, it releases a tremendous amount of gravitational potential energy, leading to a shockwave that propagates outward through the star's outer layers. This shockwave disrupts the star, causing it to explode in a powerful supernova. The outer layers are ejected into space, while the core either becomes a neutron star or, if the mass is high enough, collapses further to form a black hole.
In more massive stars, typically those with more than three times the mass of the Sun, the collapse of the core is even more extreme. As the core contracts, the gravitational forces become so intense that they overwhelm the forces pushing back, resulting in the core collapsing to a point of infinite density called a singularity. This collapse forms a black hole, a region in space where gravity is so strong that nothing, not even light, can escape from it.
In summary, the collapse of a star's core under its own gravity can lead to a supernova explosion, where the outer layers are ejected into space, and the core becomes either a neutron star or a black hole, depending on its mass.