Black holes are dangerous entities, hidden in the sides and centers of galaxies; to wait for a passer-by, who knows nothing of her existence, to be caught in her gravitational trap; To pull it to an inevitable end, astrophysics teaches us that these bodies are formed as a result of the collapse of giant stars in on themselves at the end of their lives; A supernova could leave a black hole in the center. This is — then — a good point to start, if we know at what point — during that collapse — the black hole is formed, we can use the same method and manufacture a black hole at home as a gift for our loved ones, it will be a happy surprise.
In order to do this, let’s start by correcting some concepts about the black hole. Some people think that the existence of the black hole is related to — only — the mass of the celestial body, and this is wrong. We can make a black hole from the earth, from the moon, and from a small apple as well, we will learn about that shortly; But here we must understand that the problem of the black hole is not — only — in the mass of the celestial body; But — also — in radius in relation to its mass, and to take a practical step let’s learn — now — some Newtonian physics.
Leaping from a black hole
We know from Newton’s law of gravitation that the force of attraction of one body to another is directly proportional to (i.e. increases by increasing) the mass of each of them and inversely proportional to (ie decreases by increasing) the square of the distance between them. When you stand on the ground, the force of gravity is not calculated from the product of your mass multiplied by the mass of the earth only; But we divide that by the square of the distance between you and the center of the Earth. If we assume — now — that we were able to compress the Earth in some way; so that its radius becomes ten times less than it is now, with its mass constant; The force of the Earth’s attraction to you will be multiplied by about a hundred times, which means that you will stick to the ground and almost unable to move.
The product of gravity, then, would be a very large value, compared to the attraction of the Earth to you in the normal case, because of the radius, and that is the idea, what makes a black hole so capable of attracting anything, even a ray of light itself; It is the smallest radius compared to another celestial body of the same mass. Therefore, when we replace the sun with a black hole of the same mass, the Earth will take the same orbit without any problems; Because it’s still the same distance from the center of the black hole, we’ll just die of the cold. Now that we have one part of the important information, let’s get to the other part.
Everybody in the universe has gravity, related to its mass and the distance between it and you. In order to escape its gravity, you need to jump at some speed. To escape Earth’s gravity, for example, you need to ride a rocket that jumps at 11.2 kilometers per second; That is, a speed lower than that will prevent you from escaping and bring you back to Earth again, and from Saturn you need a rocket that goes at a speed of 60.2 km / s, and from the Sun — a huge star — you will need a rocket that jumps at a speed of 617.5 km / s, and so on.
The greater the attractiveness of the body; We need more speed to escape the grip of its gravity, so it is called “Escape Velocity”, but when we want to define a black hole (1), we say that it is the body from which nothing — even the light ray itself — can escape; Since here we need to jump faster than the speed of light which is really the fastest thing in the universe, we will come back to that again shortly; But let us now go back in time to the First World War, we are now on the Russian front, one of the soldiers is a German physicist and astronomer who decided to participate in the war, although he was over forty a few months old, during the battles in 1916, a copy of Albert Einstein’s general relativity arrived at Karl Schwarzschild’s hand. Which was published a few months ago.
Schwarzschild at war
Schwarzschild himself asked our first question in this article: To what degree can we compress an object, any object, until it becomes a black hole? It doesn’t matter if it’s a star thirty times the mass of the sun, or a galaxy, or even a SUV, or maybe a bowling ball, the important thing is that we get the theoretical limit at which the attraction can’t stop, and the star collapses completely on itself, making a black hole, Here Schwarzschild first developed what we now know as the “Schwarzschild radius” (2Schwarzschild Radius). To understand what that means, more simply than what Schwarzschild means, let’s go back to the escape velocity.
It is true that equations are difficult for the lay reader; But when it becomes necessary for understanding, and it is the backbone of physics as a science, and when its rules do not go beyond several operations, the most difficult of which is multiplication and division, a ten-year-old can easily practice them; So why not? Here we can compromise a little to put one equation that will enable us to understand what can be written in 1000 words and more, what you see in front of you now is the escape velocity equation, it is the number that if we get it we will put it in our rocket computer and then press the launch button, we escape from Earth, forever!
Don’t worry too much about how that equation is deduced, and don’t memorize anything; I just want you to know that (v) in the previous equation is the speed required to escape, (r) is the radius of the planet we want to escape from, and (M) is the mass of this planet, and for (G) it is a fixed number in all equations; So we now know that that speed is always determined by the mass and radius of the planet, the greater the mass, the greater our need for a greater escape velocity, and vice versa with the diameter.
Another very strange point that we learn from the Schwarzschild equations, which is that the higher the mass of the collapsing star, the lower the density of the black hole. This seems strange; Because what we know about density indicates that density increases with increasing mass, it is equal to mass divided by volume; But the problem arises when we raise the mass of a celestial body to double, and this leads to the rise of its Schwarzschild radius to double as well, but this increases the size of the black hole — according to the simple ball-size law — to eight times, and this means that a black hole the size of a galaxy will be lighter than the density of air on Earth a thousand times.
and now; Let’s start preparing the gift
Although Schwarzschild, too, escaped bloody battles; However, he did not resist the severity of the immune pemphigoid disease and died one year later, leaving us with a great scientific legacy. During that war, he presented an accurate solution to Einstein’s equations for the field, and two papers in quantum mechanics, and it is really important to reflect on that idea, only during the battles, and in the midst of all That fear can a man of his forties achieve the greatest achievement in his life, what a paradox!
When we try to test the Schwarzschild idea on the sun — which is able to carry more than a million Earths inside it — we will find that we must compress it to become only 6 kilometers in diameter, and the Earth we need to become the size of a berry; In order to turn into a black hole, Jupiter, on the other hand, will need pressure to convert it to the size of a table tennis ball, noting that all of this must maintain the same mass, for example, the Earth will turn into a berry weighing 6 million million million million million kilograms.
Very nice, now we come to the moment of truth. All we need to know to make our black hole is — just — the mass of what we want to turn into a black hole; Let it be, for example, a huge ball of iron with a mass of 100 kilograms, we will put the number in equation (3) to get a value for the radius of Schwarzschild, it will be a number about:
.000000000000000000000001485 meters
It is then easier than we think. All you need is to compress that ball of iron, in whatever way you see fit, into a ball with a radius smaller than this “radius” above given by the Schwarzschild equation and it will turn into a black hole immediately; Unfortunately, there is a small problem. According to Hawking’s equations, that black hole will evaporate in a very short moment. But don’t worry, there is a positive side to it; For it will generate an amount of heat that can wipe out the earth completely, and here there will be no left of these fools and bug-hunters; To criticize our failure to prepare the black gift, great.
