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If a black hole attracts and engulfs light, then why doesn't the energy of the black hole increase to form a star once again? Black holes form when a star burns off its energy and collapses, so it should make sense that, since the photons engulfed in the black hole have some energy, that the black hole should reform into a stellar entity.

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You're confusing yourself. A black hole state has nothing to do with the lack of energy in a system. A star doesn't become a black hole because it can't fuse stuff anymore (i.e. the end of its energy), it becomes one because of what happens to the star after its fusion process ends**. Black holes form when a high amount of energy is concentrated at one point*, and this happens in massive stars because of the gravitational collapse of the star onto itself, when its radiation pressure (from the outward force due to nuclear fusion) goes out of balance with its gravitational force. It doesn't have anything to do with how much energy is added to or present in the system. When a black hole engulfs light or energy in general, it just becomes a slightly larger black hole, and it cannot turn back into a star as you mention.

Edit: I thought I should add in explanations for some of the things I've said.

*A system with mass energy $M$ (i.e a star of mass $M$) becomes a black hole when the spherical region it is contained in has a radius of $$\frac{2GM}{c^2}$$

($G$ is the gravitational constant, $c$ is the speed of light in vacuum.)

**Stars start out by fusing light elements like Hydrogen, and this happens faster in more massive stars. This fusion process usually abruptly stops at Iron, because the energy needed to fuse it is greater than the energy released, in simple terms. The flux of energy outward exponentially reduces, gravity takes control, and the star collapses. Depending on the mass of the star, this can lead to it becoming a neutron star or a black hole.

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  • $\begingroup$ I could be wrong but I believe the question is somewhere along the lines of 'is it possible to have pressure from inside the black so we get a back to a neutron star from a black hole?' $\endgroup$ – Otto Aug 11 '15 at 8:36
  • $\begingroup$ Possibly, but I believe the major misconception here is the one I pointed out. To me, the question sort of says that "Stars lose energy in the form of photons to become black holes, so why dont black holes turn back into stars after absorbing light?". The question also associates photons with energy, but not the mass of the black hole itself. $\endgroup$ – Hritik Narayan Aug 11 '15 at 8:42
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Your picture of "black holes form when a star's energy is ended" is perhaps somewhat correct in terms of stellar lifetimes, but it's not like a battery that runs down and can be charged back up. Think of it like this: due to gravity, any given sphere of matter at rest tries to crush inwards on itself. Something has to stop it. After all, otherwise, gravity will always want to make the object more and more compact. In your body, atoms repel each other due to electromagnetic interactions, so that keeps you stable. But your body is pretty small, so there's not a lot of gravity really. In the solar system, the planets are rotating, and so have enough kinetic energy to avoid falling any further inward. By comparison, a star has LOTS of gravitational energy and it's highly favorable for the star to shrink down to nothing. So why doesn't it? That's what the energy is--it's not about keeping the lights on, it's about holding back a collapse. For most of its life, a star manages to do this by fusing hydrogen and helium. Stars avoid collapse by exploding constantly.

This doesn't work forever. Eventually it's all out of hydrogen, and you start fusing heavier elements--maybe going through red-giant phases, or other parts of stellar evolution I won't comment on because I'm unfamiliar with them. The star can get a little more energy out of that, and stave off death. But sooner or later, the star runs out of elements to fuse. If it does any more fusion it'll lose energy rather than gain it. Now, nothing stops the collapse. So what's next? Well, the star collapses until something stops it. The question is, what? The answer depends on the mass of the star. For lighter stars, you might get a white dwarf--the collapse is eventually stopped by the "electron degeneracy pressure." The star just can't push its electrons any closer due to quantum mechanical effects. The next stage up--if the star is heavier and has enough gravity to overcome the electron degeneracy--is a neutron star, held apart by the nuclear degeneracy pressure. This is basically the same process as before, but now it's the nuclei instead of the electrons.

It's possible that none of that works. Maybe the star is truly massive, and the collapse just continues. Then you get a black hole, as it gets so dense that some small region of space becomes truly inescapable. Adding energy at this point doesn't help, because the collapse can't really be undone. There's no way to add enough energy that anything leaves the event horizon, and even if you did, it would just fall right back in. It's like asking why a demolished building won't be reconstructed if you throw a piece of drywall into the rubble.

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