100 years of General Relativity Part 5: Black Holes


This is the fifth part of the VERITAS series on General Relativity. Just to remind our readers: We are doing this series on Einstein’s Theory of Relativity to celebrate the 100th Anniversary of General Theory of Relativity. If you have missed any of the first four parts, you can read them here:

In the previous parts we discussed the fundamental idea behind General Relativity- The Equivalence Principle and its consequences. We used the equivalence principle to show that light is bent by gravity. And then we reasoned that gravity bends space-time and that objects moving along this distorted space-time seem to be moving under the influence of a force. We also saw that gravity slows down time. If you have not read the previous parts, I suggest you read them before reading this one.

We have all heard or read about black holes in popular science books/articles. The general idea is that a black hole is a region from which nothing, not even light can escape. And many of us know that black holes are formed when large stars reach the end of their lives.

The physics of Black Holes is very complex and vast. But the basic idea is that a black hole is such a deep depression in space-time that even light cannot escape. Note that anything can become a black hole if it is compressed to a high density. Every object in the universe has what is known as Schwarzschild radius and if you compress the mass of that object into a sphere of that radius you will get a black hole. For Earth the Schwarzschild radius is about 9mm( the size of a peanut). So if you want to make a black hole using Earth you will have to compress the whole mass of Earth into the size of a peanut! The Schwarzschild radius for the sun is about 3 Km.

There are three kinds of black holes:

1) Stellar black holes: When most us talk about black holes, this is the kind we are referring to. These are formed when large stars collapse under the influence of gravity. The mass of these black holes ranges from 3 solar masses( ie 3 times the mass of our sun) to several tens of solar masses. To understand how these are formed we will have to first understand how a star is formed. A star starts its life with the gravitational collapse of a clould of interstellar gas consisting mostly of hydrogen. Compressional heating raises the core temperature to such a high level that thermonuclear reactions are ignited- hydrogen is fused to form helium and this process releases energy. Lots of it! The star reaches a steady state in which the energy lost to radiation is balanced by the energy produced by thermonuclear reactions. At this time our Sun is in a steady state. But after billions of years the star may run out of hydrogen to burn. And then gravitational collapse starts again. Smaller stars end up as white dwarfs or neutron stars. But if the original star was larger than about 3 times the mass of our sun, the gravitational collapse continues forever and what we get is a black hole. Nothing, not even light can escape its pull. How are such black holes detected? By their effect on nearby stars, gravitational lensing and Hawking radiation. These effects are very interesting but I cannot talk about them in this short article. There are many objects which scientists suspect are black holes. The nearest one to Earth is known as A0620-00 and is about 3000 light years away and has a mass of about 12 times that of our sun.

2) Supermassive black holes: A supermassive black hole, as the name suggests is huge! Much bigger than stellar black holes. The mass of a supermassive black hole ranges from millions to billions of solar masses. These black holes are typically found in the centres of galaxies. Scientists believe that our own galaxy, the milky way also has a supermassive black hole in its center. These black holes are formed when the centre of a galaxy collapses under extreme gravity. However, this is not the only way: Sometimes gravitational collapse occurs when galaxies collide or merge and sometimes a galaxy forms around an preexisting supermassive black hole. The nearest supermassive blackhole to Earth is the one at the center of our galaxy. It is about 26000 light years away and has the mass of about 4 million suns!

3) Primordial Black Holes: Primordial black holes are very different from stellar and supermassive black holes. Whereas stellar and supermassive black holes can form at any time due to the collapse of stars or centres of galaxies, primordial black holes could only have been formed during the early stages of the universe. Immediately after the Big Bang the universe became a place with enormous temperature and pressure. Today we know( from the study of cosmic background radiation) that the universe at that time was very smooth but had some tiny fluctuations in the density- in other words, the matter density all over the universe was the same but there were some places where the density was different. Some of these places with density fluctuations may have undergone a gravitational collapse to create small black holes. The mass of these black holes could be as small as 10^-8 kg ( The mass of a flea’s egg)! Of course, they could also be bigger. No primordial black hole has yet been detected but some scientists think that primordial black holes may be the prime candidate for dark matter in our universe.
Now lets compare these three kind of black holes using the Hawking radiation coming out from them. In 1974 Stephen Hawking applied quantum mechanics to the study of black holes and found that they must radiate and the radiation is inversely proportional to their mass. Hawking also showed that black holes decrease in mass due to this radiation. For stellar and supermassive black holes the radiation is very small and does not cause much mass loss. In fact, for stellar and supermassive black holes the mass gain due to absorption of nearby matter completely overwhelms any mass loss to Hawking radiation. But even if the black hole did not absorb anything the rate of mass loss due to Hawking radiation for a stellar or supermassive black hole is very small over the age of the universe. But for a primordial black hole this is very different. Since the mass is very small the Hawking radiation is much more.

As a primordial black hole radiates, it decreases in mass and therefore radiates more. This results in runaway evaporation resulting in a massive explosion just before the black hole completely vanishes. Many small primordial black holes would have already exploded because of Hawking radiation. Scientists have calculated that primordial black holes of the mass of about 10^11 Kg( the mass of a mountain on earth) would be exploding now. So to detect primordial black holes, scientists are looking for explosions which are caused by Hawking radiation. These explosions would be coming from a very small area- the Schwarzschild radius for a black hole of this mass is less than a nanometer! If a primordial black hole is detected we will have very strong evidence of Big Bang, Einstein’s general relativity, the theory of how the universe evolved after Big Bang and also Hawking radiation.

The physics of black holes is very interesting. Einstein’s General theory of Relativity can tell us how black holes are formed and some of their properties but there is a lot of stuff that we still do not know. And the biggest mystery is at the centre of a black hole- a place known as the singularity. At this place the known laws of physics completely break down. This is the place of infinite gravity and curvature. This is the place where both quantum mechanics and general relativity completely fail! But we absolutely do want to understand singularities! This is because the universe at the time of the Big Bang was a singularity. So to understand the beginning of our universe we must understand singularities.

But the most interesting thing( and also the most frustrating thing!) about a singularity is that it may never ever be observed. And this is because of something known as the Cosmic Censorship Hypothesis. Basically what it says is this: all singularities are covered by black holes. So there is no “naked” singularity. In other words: An observer can NEVER observe a singularity. What happens inside a black hole stays within the black hole!

Apart from the singularity, there is another interesting place- it is known as the Event Horizon. The event horizon is the point of no escape. You can go close to a black hole and return, if you do not cross its event horizon. If anything crosses the event horizon( even light), there is no hope for it. It will be pulled into the black hole and will reach the singularity at the center. So the structure of a black hole is surprisingly simple- there is a singularity at the center and an event horizon some distance around that.

Now, let’s imagine what will happen if you cross the event horizon of a black hole. Suppose you and your friend decide to do an experiment- your friend will stay outside the black hole and you are to enter the black hole( cross the event horizon). You tell your friend that you will send him a message every 5 minutes informing him about what you see. You know that you will ultimately die but you still want to enter the black hole for the sake of scientific research . Now let’s see how things will progress. You keep moving towards the black hole and keep sending messages every 5 minutes. However, as you go closer to the black hole, your friend will see that the messages are delayed. They may come after 10 and then 20 minutes. This is because Gravity slows down time( see the last article in this series for more). When you enter the event horizon, you will see see strange optical distortions of the sky around you from the bending of light around the black hole. After you enter the black hole, your friend will not be able to get any messages- this is because nothing can escape from the event horizon. Soon you will be spaghettified – there will be enormous tidal forces—forces due to the curvature of space-time—which will squash you and you spaceship in some directions and stretch them in another until you look like a piece of spaghetti. Your spaghetti form will move to the singularity and what happens after that is a great scientific mystery. See a very interesting video about this here: https://www.youtube.com/watch?v=OGn_w-3pjMc

So black holes and their singularities are the ultimate mysteries of Physics. Nothing else even comes close.

Black Holes were not predicted by Einstein. A few months after Einstein wrote his equations of General Relativity in 1915, Karl Schwarzschild solved these equations for the simplest possible case- that of a non-rotating spherical star. Schwarzschild’s solution would later lead to the prediction of black holes. Schwarzschild’s solution contain the singularity at a particular point( now called Schwarzschild radius) but he did not realize the amazing consequences of the idea. When Schwarzschild solved Einstein’s equations, he was serving as a German soldier stationed on the Russian Front. That was the time of the first world war. Schwarzschild sent his solution to Einstein with a note that read “As you see, the war treated me kindly enough, in spite of the heavy gunfire, to allow me to get away from it all and take this walk in the land of your ideas”. He died a few months later in 1916.
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Go wondrous creature, mount where science guides
go measure earth, weigh air, state the tides,
instruct the planets in what orbs to run
correct old time, regulate the sun
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