BLACK HOLES IN DEPTH

BLACK HOLES IN DEPTH..

Black holes !! what an amazing and mysterious thing that universe has created. In my previous blog I discussed the basic things about black holes like how they are formed, types of black holes, what is inside black holes and I briefly touched upon the activity that takes place outside the black hole. Now, let us understand black holes in depth, its relationship with thermodynamics and quantum mechanics, some of the theories which enables us to unfold the mystery of this wonderful creation of the universe.

Black holes as we know is a region in space-time where gravitational attraction is so much that even light cannot escape from it. the fact that black holes and thermodynamics are inter-related came to light in 1970 when there was a mathematical discovery which showed that surface area of the event horizon of a black hole has a unique property that it increases as the additional matter or radiation falls into it. It was also said that when two black holes collide and merge to form a single black hole, surface area of the resulting event horizon is greater than sum of event horizons of original black hole. If we look closely at these properties, we will find a striking similarity between surface area of event horizon of black holes and concept of entropy in thermodynamics.

 Entropy as we know is a measure of disorder or randomness of a system, since its bit difficult to digest the concept of entropy let me give some example for it. disorder or randomness of a system refers to the spreading out of energy, for example: melting of ice cubes, a cup of hot coffee turning cold, spreading of cream in coffee. These all explain entropy where energy is being distributed to surroundings. The famous second law of thermodynamics states that entropy of a system always increases with time.

This similarity between black holes and thermodynamics was further continued by Dr Stephen hawking and his team. The first law of thermodynamics states that for a small change in the entropy of a system is accompanied by proportional change in the energy of a system. Here the proportionality constant is temperature of the system. While studying about black holes Stephen hawking and his team found similar law related to this first law. According to that law change in the mass of a black hole leads to change in the surface area of event horizon. Here the proportionality constant is surface gravity, which is the measure of strength of gravity at the event horizon. If we assume event horizon is similar to entropy then surface gravity is also similar to temperature. More over while researching they also found out that surface gravity is same at all points in the event horizon just as temperature is same at every point of a body in a thermal equilibrium.

In 1972 Jacob Bekenstein suggested a theorem about black holes where he said that, when a black hole collapses under its own gravity, it rapidly settles down to a stationary state which involves only three characteristics i.e. its mass, angular momentum and electric charge. Apart from these three properties no data is preserved by black holes. This is called ‘a black hole has no hair’ theorem. This theorem was completely proved by Stephen hawking and his team.

‘no hair’ theorem mainly implies that black hole does not contain any data except its mass, angular momentum and its electric charge i.e. its independent of its matter or antimatter, regular in shape or irregular. In other words, black holes can be formed by the large number of different configurations of matter which leaves us infinite configurations. This problem arises when we see it through classical mechanics. However, in quantum mechanics there is a different perspective. Let us take a look at this in quantum mechanics point of view.

In quantum mechanics uncertainty principle says that, a body of mass m behaves like wave of wavelength h/mc where, h is a Planck’s constant and c is velocity of light. If a cloud of particles is about to form a black hole then the wavelength of that wave should be less than the black holes that is about to form. This shows that a black hole of given mass, angular momentum and electric charge has large configurations but its finite.

This indicated that black holes have finite entropy which is proportional to surface of event horizon, it also has finite temperature which is proportional to surface gravity. This gives us a black hole can be in equilibrium with thermal radiation at some temperature other than zero. But according to classical theories there is no such equilibrium exists because black hole absorbs all the radiations and emits nothing. But in 1974 Stephen hawking proved that black holes actually emit some radiations. Consider black hole as thermodynamic system of certain temperature which is proportional to surface gravity and inversely proportional to mass. When we do this the result we get is black hole also emits particles thermally like a usual hot body of some temperature. This also proved that black holes a finite entropy at a equilibrium at some temperature other than zero.

This gave us a proof that black holes are not completely black at all instead they emit thermal radiation at a steady rate. This emission of thermal radiation is what we call as Hawking radiation. If we want to understand this emission still in deep we have to take a look at some of the theories of quantum mechanics. These theories and some of other interesting facts about black holes I will discuss in my upcoming blog.