The universe is an amazing and strange place filled with unexplained phenomena. One such phenomenon, the black hole information paradox, seems to violate a fundamental law of physics.

The event horizon of a black hole is considered the last frontier: once outside it, nothing can leave the black hole, not even light. But does this apply to information as such? Will she be forever lost in the black hole like everything else?

First of all, we need to understand that the information paradox of black holes is not related to how we are used to perceiving information. When we think of the words printed in a book, the number of bits and bytes in a computer file, or the configurations and quantum properties of the particles that make up a system, we think of information as the complete set of everything needed to recreate anything from scratch.

However, this traditional definition of information is not a direct physical property that can be measured or calculated, as, for example, it can be done with temperature. Luckily for us, there is a physical property that we can define as equivalent to information - entropy. Rather than thinking of entropy as a measure of disorder, it should be thought of as the "missing" information needed to determine the specific microstate of a system.

There are certain rules in the universe that entropy must follow. The second law of thermodynamics can be called the most indestructible of them all: take any system, do not allow anything to enter or leave it - and its entropy will never suddenly decrease.

A broken egg does not collect back into its shell, warm water never separates into hot and cold parts, and ash never collects into the shape of the object it was before it was burned. All this would be an example of decreasing entropy, and obviously nothing like this happens in nature by itself. Entropy can remain the same and increase under most circumstances, but it can never return to a lower state.

The only way to artificially reduce entropy is to introduce energy into the system, thereby "deceiving" the second law of thermodynamics, increasing the entropy external to this system by a greater value than it decreases in this system. House cleaning is a great example. In other words, you cannot get rid of entropy.

So what happens when a black hole feeds on matter? Let's imagine that we are throwing a book into a black hole. The only properties we can attribute to a black hole are pretty mundane: mass, charge, and angular momentum. The book contains information, but when you throw it into a black hole, it only increases its mass. Initially, when scientists began to study this problem, it was believed that the entropy of a black hole is zero. But if that were the case, getting something into a black hole would always violate the second law of thermodynamics. Which, of course, is impossible.

## But how do you calculate the entropy of a black hole?

This idea can be traced back to John Wheeler, thinking about what happens to an object when it falls into a black hole from the perspective of an observer far from the event horizon. From a great distance, it would seem to us that a person falling into a black hole asymptotically approaches the event horizon, blushing more and more due to the gravitational redshift and infinitely long moving towards the horizon due to the effect of relativistic time dilation. Thus, information from something that fell into a black hole would remain “encrypted” on its surface.

This solves the problem elegantly and sounds reasonable. When something falls into a black hole, its mass increases. With an increase in mass, its radius also increases, and hence the surface area.The larger the surface area, the more information can be encrypted.

This means that the entropy of a black hole is not at all zero, but on the contrary, it is huge. Despite the fact that the event horizon is relatively small compared to the size of the universe, the amount of space required to record one quantum bit is small, which means that incredible amounts of information can be recorded on the surface of a black hole. Entropy increases, information is conserved, and the laws of thermodynamics are conserved. You can disperse, right?

Not really. The point is that if black holes have entropy, they must have a temperature. As with any other object with temperature, radiation should come from them.

As Stephen Hawking demonstrated, black holes emit radiation in a specific spectrum (the spectrum of a black body) and at a specific temperature, determined by the mass of the black hole. Over time, this radiation of energy causes the black hole to lose its mass, according to the famous Einstein equation: E = mc ^ 2. If energy is emitted, it must come from somewhere, and that “somewhere” must be the black hole itself. Over time, the black hole will lose its mass faster and faster, and at one point - in the distant future - it will completely evaporate in a bright flash of light.

But if a black hole evaporates in blackbody radiation, determined only by its mass, what happens to all the information and entropy recorded on its event horizon? After all, you can't just destroy this information?

This is the root of the black hole information paradox. A black hole must have a high entropy, which includes all the information that created it. Information about falling objects is recorded on the surface of the event horizon. But when a black hole decays through Hawking radiation, the event horizon disappears, leaving behind only radiation. This radiation, as scientists suggest, depends only on the mass of the black hole.

Imagine that we have two books - about absolute nonsense and "The Count of Monte Cristo" - containing different amounts of information, but identical in mass. We throw them into identical black holes, from which we expect to receive equivalent Hawking radiation. For an outside observer, everything looks as if information is being destroyed, and given what we know about entropy, this is impossible, since it would violate the second law of thermodynamics.

If we burn these two books of the same size, the variations in molecular structure, the order of the letters on the paper, and other minor differences would contain information that could help us reconstruct the information in the books. It may come into complete disarray, but it won't go anywhere on its own. Nevertheless, the information paradox of black holes is a real problem. Once the black hole evaporates, no trace of this primordial information remains in the observable universe.

Perhaps, there is no solution to this paradox yet and it presents a serious problem for physics. Nevertheless, there are two options for its possible solution:

1.Information is completely destroyed when the black hole evaporates, which means that new physical laws are associated with this process.

2.The emitted radiation somehow contains this information, hence Hawking radiation is more than science knows.

Most of the people working on this problem believe that there must be some way by which the information stored on the surface of the black hole is "imprinted" in the outgoing radiation. However, no one yet knows exactly how this happens. Perhaps the information on the surface of the black hole introduces quantum corrections to the exclusively thermal state of Hawking radiation? Maybe, but it hasn't been proven yet. Today there are many hypothetical solutions to this paradox, but none of them has yet been confirmed.

The information paradox of black holes does not depend on whether the nature of the quantum universe is deterministic or non-deterministic, which quantum interpretation you prefer, whether there are hidden variables and many other aspects of the nature of reality. And although many of the proposed solutions include the holographic principle, it is not yet known whether it plays any role in the final solution to the paradox.