##### The Black Hole Information Paradox

Back when black holes were first analyzed by Albert Einstein, then, further detailed by Stephen Hawkings, the wonders and mysteries lying within these anomalies kept growing larger. Such is the case with the Black Hole Information paradox. In this paradox, it is stated that physical and quantum information of an item, once it enters the reach of a black hole, can no longer be recovered -- completely invisible to the universe. In Stephen Hawkings’ research, he found that as a black hole would reach the end of its life, it would emit radiation that would supposedly contain the information of whatever the hole had engulfed over its lifetime. However, when analyzed, the quantum information from the radiation would contain none of the original information of what the black hole consumed. Yet, nearly 50 years later with a lot less effort than hoped for, physicists have concluded that information can actually escape a black hole, albeit an extremely old one. In fact, it nearly instantly escapes from the black hole’s pull.

In 1992, physicist Don Page went against the popularly accepted conclusion that whatever fell into a black hole would be irrecoverable, proposed back in the 1970s by Stephen Hawkings. In his effort to prove him wrong, Page looked to quantum entanglement by finding the total entanglement between a black hole and its emitted radiation, or the entanglement entropy, creating the hypothesis that if the information was preserved by black holes, the entanglement entropy would be zero at the beginning of the process as well as at the end of its life. Thus, at some point in this process, the entanglement entropy, which rises as a black hole nears its end, would reverse until the entanglement entropy drops to zero again. With this observation, physicists were able to attempt to prove this question true or false; however, it took them nearly three decades before they were able to at least prove the Page curve to be true without any further explanation.

In 2018, Ahmed Almheiri, along with several colleagues, set out to solve the Page curve using AdS/CFT. This correspondence allows physicists to observe gravity alongside quantum physics where, in a sphere, everything that happens on the inside, or the gravity side, will have a corresponding counterpart on the quantum physics surface. However, in this space, as everything within is finite, as the black hole emits radiation, it would simply absorb it again, causing these physicists to create a sort of valve to let out the emitted radiation. In observing the quantum extremal surface, or the method which allows the comparison between the two spaces of the AdS/CFT, the physicists found that the surface area of the quantum physics surface equaled the entanglement entropy, rising in the early stages of emission of the black hole. However, as time passed, another quantum extremal surface formed within the event horizon, or the inside, of the black hole, almost as if a bubble was blown inside the black hole. Although this bubble, now storing some of the black hole’s emitted radiation, was within the black hole, it was not a part of the black hole where the black hole shelled a hollow part of the quantum extremal surface. As the black hole slowly evaporates, the quantum extremal surface within, follows suit until the black hole completely disappears, allowing the radiation held within the hollow center out, dropping the entanglement entropy back to zero.

In different tests, Almheiri was able to prove this phenomenon of information spilling out in simulations. However, past this point, it has been difficult for theorists everywhere to make further discoveries. Although the initial hypothesis has been proven, very little can be given to prove why it is that information finds itself escaping a black hole. Yet, that in itself has been the revolutionary discovery for quantum physics and black holes since Stephen Hawking’s findings in the 1970s.