Black Hole is my most favorite subject because it involves lots of spooky action, lots of calculative creativity(or creative calculation, depending on which side you're looking at).
We all know that Quantum Theory and General Relativity don't really mix well in a scientific cocktail. THEY DON'T AGREE WITH EACH OTHER. Quantum Theory was supposed to describe all physical processes of nature but does not very well good at predicting what will happen, rather just the probability, and you can only make sense of it, in the realm of science, when you add up all the probabilities, thus the sum should be equal to one. On the other hand, General Relativity only makes fuss about gravity. Unlike quantum theory, general relativity predicts exactly what will happen, and it says that what goes into the black hole never comes out(specifically when it reaches Event Horizon). According to general relativity, the information is stuck there forever(See? There is forever).
Now here comes the paradox which is a little challenging to the neural glands. It says that the black hole, surrounded by quantum fields, will radiate particles(Hawking radiation in the form of particles of zero or low mass particles, such as photons or neutrinos or gravitons) and shrink in size, and will eventually evaporate. Now if that were the case so, it violates quantum theory. Or maybe, this is a point where quantum theory changes? But since the information can't get out of the black hole, maybe the information is stored into the Hawking radiation? But it can't be so, rather than the possibility that it is being copied? But having two copies of information also violates quantum theory.
Now, some physicists propose a way to circumvent it using a concept of COMPLEMENTARITY(proposed by Leonard Susskind and folks), which states that information can be both inside and outside of the black hole, depending on one's perspective. However, this model is self-contradicting and requires a supplemental model called holography to be true as well. The idea is that the physics of the three-dimensional interior of the black hole, where gravity obviously plays a role, can instead be viewed, via a rather mysterious transformation, as physics just above the two-dimensional horizon, where it is described by two-dimensional equations that do not include gravity at all. Some physicists also conjectured String Theory(a quantum generalization of general relativity and may well be a candidate theory of all known laws of nature in the universe), which they said to be simply a quantum theory without gravity.
But as a black hole evaporates, complementarity itself runs into a serious paradox. If the outside observer sees evaporation occur without loss(or copying) of information, than an infalling observer crashes into something at the horizon whimsically called a “FIREWALL” where there wasn’t supposed to be anything. Another violation occurs, and this time it violates expectations from general relativity horrendously. It seems that if we were suppose to hinge quantum theory to be the sole description of the science behind black hole, general relativity requires a total overhaul. AGAIN, THEY DON'T AGREE WITH EACH OTHER, and there's no sign of String Theory coming to the rescue and bridging the mathematical divide. I am confused and so does everyone else.
There are lots and lots of proposals as to how to get out of this conundrum but you’re not hearing about most of them, except for Stephen Hawking’s because of his sensational pop culture status similar to X-Men's Dr. Charles Xavier, but he’s really just one of many heads tossing around this idea. In fact, this is actually the nth time Stephen Hawking keeps on changing his stand about this. So Stephen Hawking didn't solve anything yet, he just propose a new model of understanding which is not yet what science is all about. Similarly, don't expect this equation to be solved within a 10year time frame. Perhaps not even 20 years.