Black holes seem to us to be something distant, about which they sometimes make films or write in books. We rarely think about what would happen if a miniature black hole with a diameter of one millimeter appeared on the surface of our planet. About this - in our material.
There is a popular misconception associated with black holes: they are a kind of space vacuum cleaners that consume everything in their surroundings. Of course, they "feed", but their stomachs are small. The problem does not appear when they "eat", but when they "vomit" after too much dinner. That's really scary.
It's actually a little more complicated. Based on the fact that the radius of a black hole is proportional to its mass, some calculations can be made. First, let's brush up on some of the basics.
What is a black hole
A black hole is a region of space in which gravity is so strong that even light cannot leave it. The force of gravity there causes the very fabric of space-time to bend and lock on to itself. All this happens due to the compression of matter - most often, these are the remnants of a massive star - within an extremely small region.
The structure of the black hole: singularity, event horizon and Schwarzschild radius (the region from the singularity to the event horizon).
In fact, we cannot see black holes due to the fact that light cannot get out of them. It turns out that in order to leave the black hole, any object must develop a speed higher than the speed of light, which, in turn, moves at a speed of 299 792 458 meters per second. For comparison, the escape velocity to overcome Earth's gravity is only 11.2 kilometers per second. However, if we were to launch a rocket from a planet that weighs as much as the Earth, but half the diameter, then the escape velocity would be 15.8 kilometers per second. Even if the object had the same mass, the escape velocity would be higher due to its smaller size, and therefore, higher density.
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What if we shrink the object even further? If we compress the Earth's mass into a sphere with a radius of nine millimeters, the escape velocity reaches the speed of light. If this mass is squeezed into an even smaller sphere, then the escape velocity will exceed the speed of light. But since the speed of light is the cosmic limit of speed, nothing can leave this sphere.
The radius at which the mass has an escape velocity equal to the speed of light is called the Schwarzschild radius. Any object smaller than its Schwarzschild radius is a black hole. In other words, any object with an escape velocity higher than the speed of light is a black hole. To make such an object from the Sun, it will have to be compressed to a radius of about three kilometers.
A black hole has two main parts: the singularity and the event horizon. The size of the event horizon of a black hole is considered its size because it can be calculated and measured.
The horizon is also considered the "point of no return" in the vicinity of the black hole. This is not a physical surface, but a sphere surrounding a singularity that marks a boundary, the speed of escape from which is equal to the speed of light. The radius of this area is the very Schwarzschild radius.
As soon as matter is beyond the event horizon, it begins to fall towards the center of the black hole. With such a strong gravity, matter is compressed into a point - an incredibly small volume of crazy density. This point is a singularity. It is negligible and, according to modern theoretical models, has an infinite density. It is quite possible that the laws of physics we know are violated at the singularity. Scientists are actively exploring this issue in order to understand what is happening in the singularities, as well as to develop a complete theory describing what happens at the center of a black hole.
Let's do some calculations
Let's see what we can learn about a one millimeter black hole. According to calculations, such a black hole with a Schwarzschild radius will have a mass of 7 x 10 ^ 23 kilograms - more than five masses of the Moon (according to the formula R = 2MG / c ^ 2, where R is the Schwarzschild radius, M is the mass of the object, G is the gravitational constant, and c is the speed of light).
The ratio of the Earth to the Sun is three parts to one million. Thus, if the Earth were to become a black hole, its radius would be only nine millimeters. Therefore, a black hole of one millimeter would have a mass of 11% of the mass of the Earth. We would definitely have problems with the 11% extra mass on the planet.
It is enough even that the total gravity of the Earth would noticeably increase. This extra gravity would be enough to change the Moon's orbit, so it could simply fly out of its current orbit and start moving in an elliptical orbit.
The Flamm paraboloid representing spacetime beyond the growth horizon of the Schwarzschild black hole events.
Where is this imaginary black hole - on the surface, in the center of the Earth, or revolves around it? Let's assume that it is on the surface of the planet. The area of its gravitational influence would be about a third of the Earth's radius - about 2124 kilometers.
All matter in the immediate vicinity of this microscopic black hole would immediately feel strong gravity from it, and the hole, in turn, would absorb everything on the way to the center of the Earth, which it would reach in about 42 minutes from the moment it appeared. It would travel through the Earth's core and reach the other side of the Earth's surface in about the same time.
If a black hole appeared on the surface with a relative speed of less than 12 km / h, it would revolve around the Blue Planet along with its gravitational area. Simply put, it is the destruction of the earth's crust and most of its mantle. And if it's even simpler, it means the death of all life on the surface of the Earth.
Accretion rate and Eddington limit
Most of the Earth's mass around the black hole will become food and be accreted by it. Before just falling into a black hole, however, all this material will need to lose its angular momentum - which is why it will begin to rotate around it, forming an accretion disk.
This material produces a lot of heat, which will eventually be radiated. The radiation has a pressure that will slow down further accretion. Both of these effects balance each other - this is called the Eddington limit.
Accreting black hole in the artist's view
The Eddington limit also places a hard limit on the degree of accretion of a black hole. A small accretion disk would most likely have a temperature of about six thousand Kelvin - about the same as the Earth's core or the surface of the Sun.
Some frictional processes would occur between the accretion disk and the Earth's mass, as a result of which a microscopic black hole would settle in the planet's core.
Death in a black hole
In general, it would take five billion years for such a black hole to swallow the Earth. It would significantly increase the mass of the Earth. And, of course, it would immediately create a complete disorder on the planet, which in just a few hours would turn into an uninhabited cosmic patch of collapsing crust, lava, hot gases and everything else.
Life would become impossible, and the high mass of the black hole could destroy the asteroid belt. This, in turn, could lead to frequent collisions in the solar system for the next million years. The moon would continue to revolve around the New Earth (black hole), but in a very elongated elliptical orbit.
The black hole would not immediately move to the center of the Earth, but rather, it would revolve around it for a while, but in the end it would get to it. To understand how this microscopic black hole would grow in mass requires complex calculations and simulations.
All this can be summarized in the words of the world famous astrophysicist and popularizer of science Neil DeGrasse Tyson:
Vladimir Guillen