There are several ways to create a black hole, from the collapse of a supernova core to the merger of neutron stars with the collapse of a huge amount of matter. If we take the lower limit, black holes can have 2.5 - 3 solar masses, but at the upper limit, supermassive black holes can exceed 10 billion solar masses. They are usually found in the centers of galaxies. How stable are they? Which black hole will dry up first: big and voracious or small?
Is there a critical size for the stability of a black hole? A black hole weighing 1012 kilograms can be stable for several billion years. But a black hole in the 105 mass range can explode in a second and will definitely not be stable. Where is the golden mean, at which the influx of matter will be equal to Hawking radiation?
Stability of black holes
The first thing to start with is the stability of the black hole itself. Any other object in the Universe, astrophysical or otherwise, has forces that hold it together against the Universe that is trying to tear it apart. The hydrogen atom is a strong structure; a single ultraviolet photon can destroy it by ionizing an electron. To destroy an atomic nucleus, you need a higher-energy particle like a cosmic ray, an accelerated proton, or a gamma ray photon.
But for large structures like planets, stars, or even galaxies, the gravitational forces holding them are enormous. As a rule, to rupture such a megastructure, either a thermonuclear reaction or an incredibly strong effect of gravity from the outside is needed - for example, from a passing star, black hole or galaxy.
In the case of black holes, however, this is not the case. The mass of the black hole, instead of being distributed over the volume, contracts into a singularity. For a non-rotating black hole, this is one point with dimension zero. A spinning black hole is not much better: an infinitely thin, one-dimensional ring.
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In addition, all of the mass-energy content of a black hole is within the event horizon. Black holes are the only objects in the Universe that have an event horizon: a boundary beyond which it is impossible to return. No acceleration, and therefore no force, will be able to pull matter, mass or energy from the event horizon beyond its limits.
This could mean that black holes, formed in any way possible, can only grow and will never be destroyed. And they grow, relentlessly and non-stop. We observe all kinds of phenomena in the Universe, such as:
- quasars;
- blazars;
- active galactic nuclei;
- microquasars;
- stars that do not emit any light;
- X-ray and radio bursts from galactic centers;
which lead us to black holes. By determining their masses, we are trying to find out the physical size of their event horizons. Anything that collides with it, crosses it, or even touches it will inevitably fall inward. And then, thanks to the conservation of energy, the mass of the black hole will also increase.
This process occurs with every black hole known to us. Material from other stars, cosmic dust, interstellar matter, gas clouds, even radiation and neutrinos left over from the Big Bang are all sent there. Any matter colliding with a black hole increases its mass. The growth of black holes depends on the density of matter and energy surrounding the black hole; the monster at the center of our Milky Way grows at a rate of 1 solar mass every 3000 years; the black hole in the center of the Sombrero galaxy is growing at a rate of 1 solar mass in 20 years.
The larger and heavier your black hole, on average, the faster it grows, depending on the material it encounters. Its growth rate slows down over time, but since the universe is only about 13.8 billion years old, black holes grow beautifully.
On the other hand, black holes don't just grow over time; there is also a process of their evaporation: Hawking radiation. This is due to the fact that space is strongly curved near the event horizon, but straightens out with distance. If you are at a great distance, you can see a small amount of radiation emitted from the curved region near the event horizon, due to the fact that the quantum vacuum has different properties in different curved regions of space.
The end result is that black holes emit thermal radiation from the black body (mostly in the form of photons) in all directions around them, in a volume of space that basically encloses about ten Schwarzschild radii at the location of the black hole. And it may seem strange, but the smaller the black hole, the faster it evaporates.
Hawking radiation is an incredibly slow process in which a black hole with the mass of our Sun will evaporate after 10 (to the power of 64) years; the hole in the center of our Milky Way - in 10 (to the power of 87) years, and the most massive in the Universe - in 10 (to the power of 100) years. To calculate the evaporation time of a black hole with a simple formula, you need to take the time frame of our Sun and multiply by (mass of the black hole / mass of the Sun).
from which it follows that a black hole with the mass of the Earth will live for 10 (to the power of 47) years; a black hole with the mass of the Great Pyramid at Giza (6 million tons) - about a thousand years; with the mass of the Empire State Building - about a month; with the mass of an ordinary person - a picosecond. The less mass, the faster the black hole evaporates.
As far as we know, the universe could contain black holes of unimaginably different sizes. If it were filled with light black holes - up to a billion tons - they would all have evaporated by today There is no evidence that there are black holes with a mass between these lungs and those that are born in the process of merging neutron stars - in theory, they have a mass of 2.5 solar. Above these limits, X-ray studies indicate the existence of black holes in the 10-20 solar mass range; LIGO showed a black hole between 8 and 62 solar masses; also find supermassive black holes all over the universe.
Today, all existing black holes are gaining matter faster than they are losing due to Hawking radiation. A black hole with solar mass loses about 10 (to the -28 power) J of energy every second. But if you consider that:
- even one CMB photon has a million times more energy;
- 411 of these photons per cubic centimeter of space remained after the Big Bang;
- they move at the speed of light, colliding 10 trillion times per second in every cubic centimeter;
even an isolated black hole deep in intergalactic space will wait until the universe has matured to 10 (to the power of 20) years - a billion times its current age - before the black hole's growth rate falls below the rate of Hawking radiation.
But let's play a game. Suppose you live in intergalactic space, far from ordinary matter and dark matter, far from all cosmic rays, stellar radiation and neutrinos, and you have only photons from the Big Bang to chat with. How big does your black hole need to be for the rate of evaporation (Hawking radiation) and the absorption of photons by your black hole (growth) to balance each other?
The answer is obtained in the region of 10 (to the power of 23) kg, that is, approximately with the mass of the planet Mercury. If Mercury were a black hole, it would be half a millimeter in diameter and radiate about 100 trillion times faster than a solar-mass black hole. It is with this mass in our universe that a black hole would absorb as much microwave radiation as it lost in the process of Hawking radiation.
But if you want a realistic black hole, you cannot isolate it from the remaining matter in the universe. Black holes, even when ejected from galaxies, still fly through the intergalactic medium, colliding with cosmic rays, starlight, neutrinos, dark matter and all kinds of particles, massive and massless. The cosmic microwave background is unavoidable wherever you go. Black holes constantly consume matter and energy and grow in mass and size. Yes, they also emit energy, but for all black holes in our Universe to begin to deplete faster than they grow, it will take about 100 quintillion years.
And the final evaporation will take even more.
Ilya Khel