How are black holes formed?

We hear the term "black hole" really often, and we know some of its characteristics such as: it does not emit light, and it can suck things in. Except the portrait of black hole, i believe many people are wondering how is it formed. Have it been existing since the creation of universe? Or it is formed long after the formation of universe.

To many people's surprise, black holes are actually formed by the stars which burned out their fuel. When stars run out of the fuel, they will no longer generate energy and will collapsed by its own gravity because there won't be enough energy for those stars to resist the attraction of its own gravity. However, not every star can become a black hole in the end of the stellar evolution. Only the star that is 1.5 to 3 times as heavy as the sun can form a black hole because when a star collapses by its own gravity, there will be a force, exclusion principle repulsion, that resist the star to collapse. The exclusion principle repulsion can be explained by the Pauli exclusion principle. According to exclusion principle, it is impossible for two electrons, protons, and neutrons to have the same quantum state. Therefore, if a star keep shrinking, electrons, protons, and neutrons of the star will eventually occupy the same space because the volume of the star becomes very small, and the force that prevents those particles to share the same quantum state will appear. If the star is massive enough, the gravity will be so strong that even the exclusion repulsion cannot stop the collapse. When the star keeps collapsing, it will eventually become a black hole.

For those stars that are not massive enough, the collapse of gravity will be stopped by the repulsion between electrons. This kind of stars will become "white dwarf" at the final state of evolution. As for the stars that are more massive but not massive enough to form the black holes, the collapse will be stopped by the repulsion between neutrons and become "neutron stars" at the final state.

Scientists have study black holes for a long time, and I believe there are still some unsolved mysteries.  Recently, the gravitational wave is discovered. With this new discovery, scientists are able to observe black holes in a whole new way. In the next decades, I believe, the study of black holes will enter a new era.