Ch 5: Black Hole | A Brief History of Time | Summary
Curious about the black holes? Come let’s find more about it. To understand the formation of a black hole, we need to have an idea of a star’s life cycle. Collapsing of a large amount of gas into itself due to the gravitational force leads to the formation of a star. Due to contraction, the rate of collision between the atoms of the gas increases causing the gas to heat up. Eventually, the gas gets so hot that the further colliding atoms, instead of bouncing back, fuse to form helium. The heat released in this reaction is what makes the star shine. This supplementary heat also increases the pressure of the gas until it is sufficient enough to balance the gravitational attraction, and the gas stops contracting. Eventually, when the star runs out of its hydrogen and other nuclear forces, it starts to cool off and starts to contract.
In 1928, Chandrashekar worked out on how big a star could be that it could support itself against its own gravity after it had used up all its fuel. The basic idea was that in a small particle the close particles would have different velocities and would repel (according to Pauli’s exclusion) and would thus lead to expansion which was in return balanced out by the gravitational attraction. Chandrashekar realized that according to the theory of relativity the extent of repulsion cannot be more than that of the speed of light and thus calculated the maximum mass and volume for a star to support itself which was known as the Chandrashekhar limit. This meant that a star with mass less than Chandrashekhar limit would stop contracting and settle down to a white dwarf.
The answer to the question of what would happen to a star beyond the Chandrashekhar limit was first provided by Robert Oppenheimer. His work stated that with that contraction of the star the, already slightly inward-bent light cone, bend furthermore making it difficult for the light to escape. Eventually, when the star had contracted to a certain critical radius the gravitational fields become so strong that light cones are so much bent inwards that light cannot escape and according to the theory of relativity nothing can travel faster than light and hence nothing can escape from such a region which, now we call, a Black Hole. Its boundary is called the event horizon and it coincides with the path of light rays that just failed to escape the black hole. Any object that falls through the event horizon will eventually reach the region of infinite density and the end of the time.
According to the prediction by the general theory of relativity, the movement of heavy objects causes the emission of gravitational waves which cause ripples in the curvature of space and travel at the speed of light. Thus, the energy of a massive system will be carried away by these waves leading it to settle down to a stationary state. So, during the gravitational collapse of a star to form a black hole the movement and the rate at which energy is carried away would be too high to make any prediction about the black hole in general.
In 1967, Werner Israel showed that according to the theory of relativity the non-rotating black holes must be simple, perfectly spherical, and their size depended only on their mass. Roger Penrose and John Wheeler interpreted this as the gravitational waves given off by the movements involved in a star’s collapse would make it even more spherical. These statements made a picture clear that any non-rotating star irrespective of its complex shape and structure would end up as a perfectly spherical black hole after its gravitational collapse. Israel’s only dealt with non-rotating black holes. In 1963, Roy Kerr discovered a new set of solutions of the general theory of relativity that defined the rotating black holes. These “Kerr” black holes rotate at a constant rate and their size and shape depended only on its mass and rate of rotation. If rotation is found to be zero then it’s a perfectly spherical body and in case of non-zero, the black hole bulges out at its equator, faster the rate of rotation, more the bulge. Thus, it was conjectured by Kerr’s solution that any rotating body that would collapse to form a black hole would eventually settle down to a stationary state.
There were many opposing to the concept of the black hole. In 1963, Maarten Schmidt measured the red-shift of a faintly star-like object. The shift was found to be too large to because by the gravitational field cause if this would have been the case then the object would be so massive and so near to us that it would disturb the orbits of the planets in the solar system. For an object to be visible at such a distance, it must emit a huge amount of energy. The only mechanism evident in this case was the gravitational collapse of not just a star but a whole central region of the galaxy and this provided the conclusive evidence of black holes. Cygnus X-1 in our galaxy and Magellanic Clouds in the neighbouring galaxies are the evidence for black holes. The number of black holes may be greater than the number of visible stars. The extra gravitational attraction of these black holes is the reason for the rate at which our galaxy rotates.
One could also consider the formation of low-mass black holes. But these can only be formed when exposed to large external pressure. A little more practical approach for this could be that these low-mass black holes might have been formed in the high pressure and temperature of the very early universe due to its irregularities. These irregularities would have accounted for the formation of a significant number of ‘primordial’ black holes i.e., if we could determine the number of primordial black holes present in the universe, we could learn a lot about the early universe!
[ A chapter’s summary from the great book A Brief History of Time -By Stephen Hawkins].
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