Nobel Prize in Physics, 2020
M.V.N. Murthy, Chennai

Stars are born ... stars die. How does this happen? The key ingredient is the gravitational force. A star is formed in regions of galaxies where there is enough material. Gravity pulls the matter (mostly hydrogen in space) together to form an approximately spherical object because gravity acts the same way in all directions. This is our proto-star. As gravity continues to compress the matter further, nuclear fusion begins to take place in the core of the star, where the hydrogen gas is converted to helium through a set of processes that releases energy in the form of heat.
Hot gases expand outwards, and hence the heat produced at the center of the star creates a counter-pressure to gravity. This keeps the star burning for a very long time with the outward pressure balancing the inward gravitational forces. The star remains in equilibrium for tens of million to billions of years. As the core of the star gets hotter, further nuclear fusion takes place, with heavier elements such as carbon, nitrogen, oxygen, and eventually silicon and iron being formed.
Stars such as our Sun will soon exhaust their nuclear fuel and die out. In heavier stars, 10-20 times heavier than our Sun, once the nuclear fuel is exhausted, gravity takes over and compresses the matter even further, until it cannot be compressed any further. The outer layers of the star then explode in a supernova explosion, and the dense core of the star, called neutron star, is left behind.
If the initial star was much heavier than 20 times the mass of our Sun, the compresssion cannot be stopped and the star may end up as a Black Hole. Therefore in the scheme of things in the cosmos, Black Holes are not rare. They are as common as other stellar objects, only more exotic.
What is a Black Hole? It is a region of space where gravitational forces are so strong that nothing can escape from it. Any object that comes close enough to a Black Hole is captured for ever. So this is very different from our usual experience of gravity.

Gravity on Earth
Consider throwing an object, say a piece of stone vertically upwards. It will go up to a certain height and falls back. The height keeps increasing as the initial speed increases. But the stone keeps falling back to the surface of the earth due to the gravitational pull exerted by the earth. This is part of our daily experience. What happens if we keep increasing the speed? We are imparting larger amounts of kinetic energy initially.
At a certain speed, an object thrown vertically upwards can actually escape the gravitational pull and go free. We know this since this what rockets do to put satellites in to outer space. This minimum speed required to escape the gravitational pull of any celestial object is called escape velocity. The expression for the escape velocity to escape from an object (Earth or any star) with mass M and radius R is given by v2=2GM/R, where G is the Universal Gravitational constant (see Box).

BOX on Escape Velocity and Black Holes
It is easy to calculate the escape velocity with a little knowledge of gravitational force. Objects fall back to earth because the potential energy (due to gravity) is greater than their kinetic energy (due to their velocity), which is KE=mv^2/2 for an object of mass m and velocity v.
To escape the gravitational pull the body must have enough kinetic energy to overcome the gravitational pull. Escape velocity is the minimum velocity at which the kinetic energy of the object is equal to the gravitational potential energy. This is given by Newton's equation for gravity, PE = GMm/R, where G is the universal gravitational constant, G=6.7 x 10^{-11} Nm^2/kg^2, M is the mass of the Earth, M=6x10^24 kg (that is the source of the gravitational potential), and R the distance between their centres. Here we have to actually add the height of the object above the ground to R, which we neglect since it is so small compared to the radius of the earth, R=6400km.
Equating PE=KE, we find the escape velocity is v^2=2GM/R. For the Earth, this evaluates roughly to v=11 km/s.
(The gravitational constant can be found from knowing Earth's mass, M, its radius, R, and the acceleration due to gravity on Earth's surface, g=9.8 m/s2, as g=GM/R2.)
You can see that the escape velocity is independent of the mass of the object m thrown upwards.
Notice that if we keep increasing M while R is a constant, v keeps on increasing. We may therefore reach a stage when the gravitational pull becomes so strong, and escape velocity so large, that the stone thrown vertically upwards may never escape the pull of such a heavy (large M) and dense (small R) celestial object. Such an object may be called a Black Hole since almost nothing can escape no matter how light or heavy the object is.
END OF BOX

Newton and Einstein
We know that there is no limit to speed in Newtonian Mechanics. However, Einstein's theory of relativity tells us that there is a maximum speed which is the speed of light, c=300,000km/s. Nothing can exceed this value. Naturally this is the limit on the escape velocity too. We can ask, what should be the radius R of a celestial object of mass M so that the escape velocity is this value, c. Inverting the equation for escape velocity, we get, R_S=2GM/c^2, which is called the Schwarzschild radius after the person who first realised its importance.
If an object of mass M attains this radius then the escape velocity is the maximum speed of any object. Since nothing can go at speeds greater than this speed, there is no escape for matter trapped inside the Schwarzschild radius. Thus if we somehow start compressing a celestial object it becomes a Black Hole when it reaches the size of Schwarzschild radius! This is actually a very small radius. For example the Schwarzschild radius of the Earth is 8.87 mm whereas for the Sun it is 2.95 kms. Imagine compressing the Earth to few mm!
While this argument illustrates the idea of a Black Hole using simple Newtonian mechanics, it is not entirely consistent since the interior of highly dense objects cannot be described by Newtonian Mechanics. In fact, Black Holes were not discussed until the advent of Einstein's general theory of relativity. The ideas behind this theory are very complex and involve thinking of space and time as a unified entity in which matter (or energy) can distort or cause the curvature of space-time. That is, the space around us is stretched or bent because we are made of matter! This is hardly visible since our masses are small. But it is very prominent for massive objects. Immediately after Einstein formulated his equations, Karl Schwarzschild realised that Black Holes indeed arise as solutions of Einstein's equations.

Bending of light
It has been observed that light rays bend in the presence of a massive object like the Sun. The amount of bending is a prediction of Einstein's theory. Suppose we replace the Sun by objects whose gravitational pull keeps on increasing while its mass is constant, by reducing its size. The light keeps on bending more and more until at precisely the Schwarzschild radius, the light bends so much that it falls back into the gravitating object itself. So we have a Black Hole that gobbles up every thing around and nothing escapes from it. The surface of the Black Hole which divides the inside and outside is called the Horizon whose radius is now the Schwarzschild radius.

Do Black Holes really exist?
Initially it was thought that the concept of Black Hole is simply a mathematical construction with special conditions that may not occur in Nature. Not many believed that it can be realised in actual practice. It was Penrose and Hawking in the nineteen sixties who showed that Black Hole is not a special case but it is a solution that is valid under very general circumstances. The credit for taking Black Holes seriously, not just as mathematical curiosities, goes to Roger Penrose and Stephen Hawking. Unfortunately, Hawking passed away in 2018.
So Black Holes, which started as a mathematical curiosity in the beginning turned out to be more common than we expected by 1970s. But how does one observe them? They do not emit light. We cannot send a probe since that too will disappear -- after all it is a "Black Hole". We need not despair since Black Holes affect the objects around them through gravitational force. Depending upon the initial path, a stellar object may simply go around a Black Hole just as a planet goes around the Sun. In this case we cannot see the Black Hole in the center. But an orbiting star with nothing in the middle clearly indicates the existence of the Black Hole. The speed of the star and the size of the orbit has the information about the mass of the Black Hole. It may even so happen that a nearby star moving towards a Black Hole may be gobbled up-- disappearance of a star is another evidence of Black Holes.

Sagittarius A* and the Milky Way Galaxy
Around the 1990s it was discovered that there exists a super-massive Black Hole at the centre of our own Milky Way Galaxy. This was independently discovered by Reinhard Genzel and Andrea Ghez, who thus won the Nobel prize in Physics this year. They observed the star S2 (or S-O2) which had a very high orbital speed of less than 16 years. Also, it was orbiting around a region called Sagittarius A* which is a very bright and compact radio source. As can be seen from the figure, the entire orbit of S2 was mapped very precisely. From this, it was shown that Sagittarius A* is the location of a super-massive Black Hole with a mass about 4.3 million times that of our Sun! The Black Hole which was in hiding for so long had been discovered.
There is some thing that we still do not understand in spite of the work done by these and many other giants in the field. What happens after matter falls into a Black Hole? How does it behave? It will be billions of times more dense than the densest matter that we know. Perhaps there will be no atoms, nuclei. It will be a primordial soup of the most fundamental particles that we know or perhaps do not yet know. At such densities the gravity is so strong that even Einstein's theory cannot describe their behaviour. Thus we know the laws of physics that govern matter outside the horizon of a Black Hole; its inside is still a mystery to be unfolded.