BLACK HOLE THERMODYNAMICS

-   An Introduction

Black Holes are and have been an anomaly since their prediction.  They are not new to the world of Physics, infact it was Laplace who first predicted them

"A luminous star, of the same density as the Earth, and whose diameter should be two hundred and fifty times larger than that of the Sun, would not, in consequence of its attraction, allow any of its rays to arrive at us; it is therefore possible that the largest luminous bodies in the universe may, through this cause, be invisible." – Pierre Laplace, The System of the World, Book 5, Chapter VI (1798).

The existence of Black Holes was later Mathematically Formulated as a solution of the GR equations.  Since then many Astronomers have been trying to point out Black Holes in our Universe. Theoreticians have been playing with the Mathematics of Black Holes to find elegant solutions to many problems like the beginning and ending of the Universe, Time Travel etc… .  What is so exciting about Black Holes that makes them controversial? In this article, we shall see a brief introduction to the Thermodynamic Laws that govern Black Holes…

How are Black Holes Formed?

A Star exists because the pressure developed inside the star due to Fusion of the Hydrogen in the star balances the Gravitational Attraction of the core of the star. Since these 2 balance each other the star maintains its size until the Hydrogen is present in it… Only until the Hydrogen is present in it. After all the Hydrogen in the star has been converted to Helium, the pressure inside the star is no longer able to compensate the Gravitational Attraction and hence the star reduces in size. This contraction further increases the temperature inside the star, that the Fusion of Helium begins and this develops so much pressure that the Pressure exceeds the Gravitational Attraction and the star expands. This stage when the star is huge is called a Red Giant stage. After this stage, when all the Helium is used up, the Star again collapses and now there are 2 possibilities that can happen:

a)       If the mass of the Star < 1.2 times Mass of the Sun: now, the mass content of the star is not sufficient to start another Fusion and thus the star cools down to a White Dwarf star that emits radiation to wear of its internal Energy.

b)       If the mass of the Star > 1.2 times the Mass of the Sun: now, the Star has enough mass to overcome the White Dwarf stage and thus another fusion starts and it proceeds until…

(i)      If the mass of the star is < 3 times and > 1.2 times the Mass of the Sun, then, the Star at one point of time explodes to excess pressure inside the star (Supernova Explosion) and a Rotating Neutron Star (Pulsar) is left.

(ii)     If the mass of the star > 3 times and > 1.2 times the Mass of the Sun, then there is so much matter that Gravity dominates every inch of the Star and the Star collapses into itself. i.e. it undergoes successive contractions, upto a stage when there is so much concentration of mass in that region of space that a very high gravitational field is set up that is so powerful that not even light can escape from it.

This radius where the Gravitational Potential Energy of the Collapsed Star equals the Kinetic Energy possessed by light such that not even Light can’t escape beyond this region is called Schwarzschild Radius (r_bh).

                         At the Schwarzschild Radius,

                           Let the Kinetic Energy possessed by light =  K = (p*c)/2 [Mass equivalent for light = p/c]

                           p is the momentum of a Photon.

                           The Gravitational Potential Energy at r_bh  = P = [GM(p/c)]/ r_bh  where, M is the Mass of the Star

                             Thus, when K = P,

                                                           r_bh = (2GM)/c²

Below this radius, Light an never escape and above this radius the Gravitational Field of the Collapsed Star can be experienced. This effect due to which even Light cannot escape the gravity of the star makes it invisible to us, thus appearing invisible to us. Hence the name Black Hole (coined by John Archibald Wheeler).