Everything you need to know about black holes

Have you ever experienced a situation that sparked a sense of terror and fascination at the same time? I already… and went to see the image above: the Gargantua black hole of the movie Interstellar.

Gargantua is the only chance for the human species to escape extinction, but to achieve this goal the protagonist must enter the black hole even if it means certain death. The total surrender to humanity and the encounter between a man and the sublime mystery of the universe aroused in me these seemingly contradictory feelings. So I decided to write this text to show you how wonderful and terrifying the black hole is at the same time.

There are two types of black hole: stellar and supermassive. The first is formed when a star with more than 8 solar masses collapses in gravity, while the second arises when huge clouds of gas or star clusters collapse. The stars remain in a fine balance between the radiation released by the star nucleus and gravity, which, according to Albert Einstein’s findings, is an effect of the curvature of space-time (the “fabric” that forms our universe) caused by the mass of a body.

Representation of the curvature of spacetime caused by the masses of the earth and sun.

Remember that we are in a three-dimensional space, so the metaphors used in this text only serve to better understand the universe. Never confuse representation with the thing itself. As long as there are nuclear reactions the star will remain stable, but there comes a time (billions of years) when nuclear fusion no longer generates energy and the star contracts as it has been defeated by gravity itself. Such failure is called gravitational collapse.

But what are stellar black holes? And how do they form? Well, the answer to this last question depends on the mass. If it is too high, the particles will be unable to prevent the star’s core from collapsing below the Schwarzschild radius, thus turning it into a black hole. But, you might be wondering: Got it, but what is Schwarzschild’s ray? This tells us what the radius (the distance from the center to any point of the circumference) of a body should be so that it does not become a black hole and therefore remains stable. Example: The Earth’s Schwarzschild radius is 9 mm, so turning it into a black hole requires a force to compress it below this value. Thus any body can become a black hole as long as the mass is contracted to a point whose radius is smaller than Schwarzschild’s for that object.

In the black hole the Schwarzschild Ray represents the distance between the singularity and the event

The star corpse, which remains of the star after the gravitational collapse, whose radius is smaller than Schwarzschild’s, becomes so dense that it “sinks” deeper and deeper into the fabric of the universe until it becomes a gravitational singularity: a dot infinitesimal in which the laws of physics we know are not applicable. Being so dense the uniqueness causes the spacetime to bend over itself creating a spherical region in spacetime possessing immense gravitational force from which nothing can escape; at least not the same way you entered. For the set composed of the uniqueness and the circumference it forms around it is called the black hole. Since we can only speculate about uniqueness, so physicists have decided that the best thing to do is to study the surface of the black hole in which very crazy phenomena occur.

Deformation in spacetime caused by the following celestial bodies: Sun; White Dwarf; Neutron Star and Black Hole. There is also information in the image that when turning into a black hole the radius of the Earth would be 0.7 inches.

A ball is formed by a flat surface and this is all we can know of such an object. The same is true with a black hole. The totality of what we are able to know about such a celestial body lies on its two-dimensional surface called the event horizon. This name is due to the fact that it constitutes the imaginary boundary of the black hole beyond which an external observer can know nothing about the events that occur there. This is made clearer by analyzing the fire wall paradox. This paradox describes what would happen if one observer fell into a supermassive black hole while another observed it. The supermassive was chosen because it is the only type of black hole that has a lightning bolt that allows a human to not die before crossing its event horizon. There are two astronauts, Alice and Bob, near the supermassive black hole Sagittarius A* that actually exists and is in the center of the Milky Way. Alice heads into a space capsule that is about to cross the event horizon, while Bob watches her through a telescope attached to the spaceship.

From his perspective, Alice will approach the ever-slower event horizon until at one point it would appear that she froze in time, turned very red and eventually disappeared. Whereas from Alice’s perspective nothing would change at first as it crossed the event horizon, except that if she looked out of the black hole she would see the whole universe moving away at a high speed nearly the speed of light. Such a paradox could be the result of an optical illusion caused by the peculiar properties of the black hole. But both situations, as absurd as this may be, are equally true. What causes Alice and Bob’s observation of the same celestial body to result in two totally different physical realities? And what features of the black hole cause Alice to watch the universe drift away at a high speed, while Bob sees it stop in time as it approaches the event horizon, turns red and disappears? These were the questions that arose after I came across the information paradox experienced by the two hypothetical astronauts that I will seek to answer in the next paragraphs.

However, one must first understand how the image is formed in the human eye. The light after reaching a body is reflected and penetrates the human eye in which, by action of the brain, transforms the light into image. When Alice crosses the event horizon, the conceptual boundary that once passed cannot be returned, the photons (particles of light) that touched her on reflection get trapped in the black hole and do not reach Bob’s eyes preventing her from falling. Create a picture of her. That’s why she disappears. As for time, I have repeatedly said that the black hole is the region of spacetime that has bent over a gravitational singularity. In such a celestial body time has been deformed in such a way that as you approach it everything slows down until you have the feeling that it no longer exists.

To understand how this occurs the phenomenon in which Alice sees the universe moving away from her at a high speed requires two things. The first is that while not being in a black hole the rest of the universe is actually moving away from you at 74kps per megaparsec. This would be noticeable if you could visualize the edge of your cosmological horizon (the limit of the observable universe) being stationary, as moving the distance between you and your cosmological horizon remains the same as in the Achilles paradox and the tortoise. The second is that everything that goes into a black hole, including the reflected light from Alice’s entire observable universe, converges on the astronaut’s uniqueness and visual field. Thus, when the photons cross the event horizon and flow to the focal point (area where light rays are capable of forming an image) of Alice forms before her the image of the entire observable universe compressed into a single point. To view this image I recommend reading the short story The Aleph of Jorge Luís Borges. With the observable universe so close to her Alice is able to see the cosmological horizon; hence the sight of everything moving away from her at a high speed. And why does it turn red as it approaches the event horizon?

The answer to this question was given to us by Stephen Hawking, who, by combining the area of ​​quantum mechanics with that of general relativity, discovered that something could come out of the black hole in the form of thermal radiation, called Hawking Radiation, because of quantum fluctuations. vacuum. These happen due to the continuous movement near the horizon of events of pairs of particles and virtual antiparticles (the adjective is due to the fact that such bodies exist for a very short time) that repel each other. The antiparticle is drawn into uniqueness by releasing its positive energy partner into outer space. This results in the gradual loss of energy and mass by the black hole that after trillions of years will disappear. But how is this possible if the vacuum is the absence of something? In fact, the vacuum is not as empty as we have been taught, as this is contrary to the Uncertainty Principle formulated by physicist Werner Heisenberg. Such a theoretical formulation, already proven by experiments, postulates the impossibility of an observer to simultaneously measure the position and velocity of a particle. If absolute vacuum were possible the energy of a particle would be zero so that both its velocity and position would have the same value; This means that both could be measured which is contrary to the Uncertainty Principle. The fact that a black hole releases radiation has led Stephen Hawking and Jacob Bekenstein to discover that there is entropy in it and that it is deeply linked to the concept of information. But what is entropy, information, and how do these two relate in a black hole?

Black holes are the largest hard drives in the universe, although so far we don’t know how to access the data on them.

In high school, physics teachers teach that entropy is a thermodynamic quantity related to measuring the disorder of a physical system. To say that there is more disorder in a puddle than in an ice cube is a subjective interpretation. But if it is not the clutter of a system that is measured, then what is it? Thanks to the work of physicist Ludwig Boltzmann (founder of statistical mechanics) and mathematician Claude Shannon (father of information theory) the scientific community has found that entropy measures the probability of all possible states that can be adopted by the particles that make up a system. . In other words, entropy is the measurement of the probability of constituent elements distributing themselves in any possible configuration in a given system. Information is the property that defines the arrangement, state, and position of elementary particles. Thus, the greater the information of a system, the greater its entropy. Jacob Bekenstein and Stephen Hawking continued their research and found that the entropy, and therefore the particle information, of a black hole lies entirely on its event horizon. This is contradictory, since in the whole universe the increase in entropy results in an increase of the volume of a system and not of its surface area. The pair decided to calculate the entropy of a black hole. For this they sought to answer the following question: what should be the smallest possible area to be occupied by a single bit, minimum unit of information that may be equally likely in one of two configurations (0 or 1), so that the event horizon be fully covered? The answer is that not only the black hole, but the entire cosmos is made up of endless units of information whose area is measured in Planck length whose value is 0.00000000000000000000000000000016 meters. It is inconceivably small.

Each entropy unit on the event horizon is formed, according to the laws of physics, by four areas of Planck.

This new understanding of black holes provided physicists with a more solid basis for investigating the universe and answered the question I asked in this text as to why Alice and Bob experienced such disparate physical realities. Being inside a black hole Alice interacts with more bits than Bob resulting in distinct physical realities. However, the discovery of Hawking Radiation brought to the scientific community a new problem situation as in the process of “evaporation” from the black hole something very important apparently is deleted from the universe: information. But this, according to quantum mechanics, cannot be lost. From this arises the paradox of information. As you may have noticed, Alice and Bob are metaphors for describing what happens to particles falling into the black hole according to general relativity and quantum mechanics, respectively. This paradox has been resolved by the understanding that all the entropy of a black hole lies on its surface.

Infographic about the information paradox. On the left is the description of general relativity about the black hole that constitutes the reality lived by Alice, while on the right is the reality lived by Bob which is described by quantum mechanics.

According to general relativity, information that crosses the event horizon is lost forever, but quantum mechanics postulates that information is indestructible. That is, it is recoverable so that the state of any system is reversible; even though the technology for this has not yet been created. In other words, I could recreate the trees from their ashes through technology that can reverse the process. The contradiction between two equally true approaches to reality (general relativity and quantum mechanics) sparked a debate in the 1990s between Stephen Hawking and Leonard Susskind. He argued that information was lost forever as it crossed the event horizon, while it argued that such loss was impossible. During the time of the debate theoretical works established the relationship between entropy and information. Susskind and his friend Gerard ‘t Hooft realized that if the entropy of a black hole, a three-dimensional object, is on a two-dimensional surface meant that the same is true of information. Here is the holographic principle: the information of three-dimensional things falling into a black hole is encoded on its two-dimensional surface. Thus information is not lost, it is only inaccessible because of our current technoscientific limitations.

The information paradox had finally been resolved, but Stephen Hawking did not accept such a solution since it was an unsupported conjecture, and because Susskind and Gerard ‘t Hooft extended the holographic principle of the black hole to the entire universe. They asserted that if everything that falls into a black hole, which is a part of spacetime, is stored in the event horizon, then everything in the universe is encoded on a two-dimensional surface which is the cosmological horizon. The universe is therefore a hologram. This does not mean that our reality is false, for from a scientific point of view the hologram and the projecting surface are equivalent so that naming that or this false is a subjective choice. Most of the scientific community did not accept until Argentine physicist Juan Maldacena appeared in the scientific community. Through equations he discovered a mathematical correspondence between a holographic universe and the surface responsible for projection. Such an embodiment is called an AdS/CFT correspondence. Given this new fact Hawking recognized defeat and changed his own ideas as every human being should do.

The holographic principle has important philosophical implications for the human species: since the universe and everything in it has a three-dimensional projection of information encoded on a two-dimensional surface, then where are we really? Who or what really are we and what is our true form? The answers lie in the black holes where general relativity and quantum mechanics meet. It is up to us to dare to plunge into the profound mystery of existence, for in this we will find incalculable treasure.



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