When do black holes become unstable?

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There are several ways to create a black hole, from the collapse of a supernova nucleus to the fusion 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 located in the centers of galaxies. How stable are they? Which black hole runs out first: big and voracious or small?

Is there a critical size for black hole stability? A black hole weighing 1012 kilograms can be stable for several billion years. But a black hole in the mass range 105 could explode in a second and definitely not be stable. Where is the Golden mean at which the flow of matter will be equal to the radiation of Hawking?

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 holding it together against the Universe that is trying to tear it apart. A 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.

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But for large structures like planets, stars, or even galaxies, the gravitational forces that hold them are enormous. Typically, to break such a megastructure, you need either a thermonuclear reaction or an incredibly strong impact of gravity from the outside — for example, from a passing star, a black hole or a galaxy.

In the case of black holes, however, it is not so. The mass of a black hole, instead of being distributed by volume, is compressed into a singularity. In a non-rotating black hole, this is one point with zero dimension. A rotating black hole is not much better: an infinitely thin, one-dimensional ring.

In addition, all the contents of the mass-energy in the black hole are 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, which means no force can pull matter, mass, or energy from the event horizon beyond.

This may mean that black holes, formed in any way possible, can only grow and will never be destroyed. And they grow, inexorably and non-stop. We observe all kinds of phenomena in the Universe, such as:

  • quasars;
  • blazars;
  • active galactic nuclei;
  • microquasars;
  • stars that emit no light;
  • x-ray and radio bursts from galactic centers;

which lead us to black holes. Determining their masses, we try to find out the physical dimensions of their event horizons. Anything that collides with it, crosses it or even touches it, will inevitably fall inside. And then, thanks to energy conservation, the mass of the black hole will increase.

This process happens to every black hole we know. Material from other stars, cosmic dust, interstellar matter, gas clouds, even radiation and neutrinos left over from the Big Bang — everything goes 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 is growing at the speed of 1 solar mass in 3000 years; the black hole at the center of the Sombrero galaxy is growing at the speed of 1 solar mass in 20 years.

The larger and heavier your black hole is, on average, the faster it grows, depending on the material encountered. Over time, the rate of its growth slows down, but since the Universe is only about 13.8 billion years old, black holes grow perfectly.

On the other hand, black holes do not just grow with time; there is also the process of their evaporation: Hawking radiation. This is due to the fact that the space is strongly curved near the event horizon, but straightens when removed. If you are at a great distance, you can see a small radiation emitted from the curved region near the event horizon, due to the fact that the quantum vacuum has different properties in different curved areas of space.

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The end result is that black holes emit thermal radiation from the black body (mainly 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.

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Hawking radiation is an incredibly slow process, in which a black hole with the mass of our Sun will evaporate in 1064 years; a hole in the center of our milky Way — in 1087 years, and the most massive in the Universe — in 10100 years. To calculate the evaporation time of a black hole by a simple formula, we need to take the time frame of our Sun and multiply by (the mass of the black hole/the mass of the Sun)3.

From this it follows that a black hole with a mass of the Earth will live 1047 years; a black hole with a mass of the great pyramid in Giza (6 million tons) — about a thousand years; with a mass of the Empire state building-about a month; with a mass of an ordinary person-picosecond. The smaller the 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 — all of them would have evaporated by now There is no evidence that there are black holes with a mass between these lungs and those that are born in the process of fusion of 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 range of 10-20 solar masses; LIGO showed a black hole of 8 to 62 solar masses; they also find supermassive black holes all over the Universe.

Today, all existing black holes gain matter faster than they lose due to Hawking radiation. The black hole of the solar mass loses about 10-28 j of energy every second. But when you consider that:

  • even a single photon of the background radiation is a million times more energy;
  • 411 such photons per cubic centimeter of space left 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 in the depths of intergalactic space will wait for the universe to Mature to 1020 years — a billion times its current age — before the rate of growth of the black hole falls below the rate of Hawking radiation.

But let’s play a game. Let’s say you live in intergalactic space, away from ordinary matter and dark matter, away from all cosmic rays, stellar radiation and neutrinos, and you only have photons left from the Big Bang to chat with. How big should your black hole be to make the evaporation rate (Hawking radiation) and photon absorption by your black hole (growth) balance each other?

The answer is obtained in the region of 1023 kg, that is approximately the mass of the planet mercury. If mercury were a black hole, it would be half a millimeter in diameter and emit about 100 trillion times faster than a black hole of solar mass. It is with such a 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 can’t isolate it from the remaining matter in the Universe. Black holes, even when ejected from galaxies, still fly through the intergalactic environment, colliding with cosmic rays, star light, neutrinos, dark matter and all sorts of particles, massive and massless. Space microwave background is impossible to avoid wherever you go. Black holes constantly absorb matter and energy and grow in mass and size. Yes, they also radiate energy, but it takes about 100 quintillion years for all the black holes in our Universe to begin to Deplete faster than they grow.

And the final evaporation will take even more.


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Updated: November 24, 2018 — 5:30 pm

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