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The Theory of Relativity and Black Holes

Question:

Discuss about the Black Holes and Hawking Radiation for Quantum Mechanics.

While the whole scientific world thought that black holes would stay forever, a talented young man from England invented a theory in 1974. The theory was dubbed Black Hole Explosion and was a combination of both Relativity and Quantum Mechanics. The theory of Black Hole Explosion stated that black holes are not as black as we think but they radiate energy known as Hawking Radiation.

Hawking presented his idea in 1970 and he was not sure about the method to measure the entropy of black hole but a young student from Preston University named Jacob Bekenstein suggested that if the black hole has entropy, the surface area of the black hole which is known as the event horizon will be the measure of its entropy and if any matter enters the black hole the size of the event horizon will increase (Blundell, 2015).

Stephen Hawking was one of the brightest and most innovative minds of his time. His limitless creativity has made tremendous contributions to a plethora of remarkable discoveries that deserve every ounce of praise despite his body being paralyzed by Amyotrophic Lateral Sclerosis. His life was an ongoing journey in which he solved many mysteries of the universe. One of such mysteries was about the strangest objects in the space known as black holes. He did not do the actual discovery of the black holes but rather was the one who described their influence on the environment using mathematical approaches (Blundell, 2015).

“One of the principal contributions of Hawking to modern physics is taking black hole into mathematical terms and expressing its influences on the environment,” said Paul Delaney, Director of the York University Astronomical Observatory and Senior Lecturer, Astronomy and Space Exploration.

"To understand the concept of Hawking Radiation, we need to understand the stars, black holes and how Hawking Radiation works in conjunction with some of the most known theories," he said.

It all goes back to 1915 when Einstein came up with the theory of Relativity, one of the greatest discoveries ever made in the field of physics. He discovered that gravity is a factor of the space and massive objects like the star cause distortion in the space (Susskind, 2014). The distortion caused makes the space around them curve hence bringing about an effect on the motion of the bodies which are close to them.

A simple example is the sun that is so massive that it makes up to 99.86 percent of the total mass of our solar systems and the distortion caused by this mass in the space is the reason that all the planets and the countless asteroids revolve around it (Ong, 2015).

The theory of relativity brought one more idea along with it, the idea that if a star is as heavy as a mass of ten suns or more, it can collapse under the pull of its own gravity to form a black hole. “The black hole is formed when the star dies in a supernova explosion under the influence of its own gravity,” said Professor Delaney.

Entropy and Event Horizon

My story will show that black holes are not as black as we think but they radiate energy known as Hawking Radiation as will be explained in details in the later stages of this discussion.

He farther explains that stars are basically nuclear furnaces composed of hydrogen gas and fuses two hydrogen atoms into one helium atom and produces a tremendous amount of energy. This nuclear reaction takes place inside the core and the resulting energy floes out from the core. The life of the star is determined by the constant struggle between the gravitational pull of its core and the energy released by the nuclear fusion at its core (Ngampitipan, 2014).

The gravitational force of the black holes is very huge such that they distort the space in such a way that the escape velocity from their gravitational pull exceeds the speed of light. This means that not even light can escape it once it goes beyond the event horizon known as the point of no return.

Most of the scientists believed that objects like this can’t exist in nature for quite a long time after this prediction (Hawking, 2016). They as well believed that another occurrence will prevent it from happening but it was, later on, proved over the years by the combined work of Karl Schwarzschild, John Wheeler besides numerous other astrophysicists that black holes do exist but still it was a topic of debate. Black holes were still united mysteriously and most of the scientists still trying to unfold the mystery.

Hawking developed his interest in the theory of relativity and black holes when he started his Ph.D. at the University of Cambridge despite being diagnosed with ALS, his determination superseded the disease (Bailyn, 2014).

During his research on black holes, he noticed that the size of black holes can only increase or remain at the same size but cannot decrease in size since it is obvious that black holes swallow all any object that comes too close to them. If they swallow more materials or matter, their mass and entropy increases.

The search was similar to the second law of thermodynamics which starts that the entropy of an isolated system can never decrease but instead will stay either constant or increase. Entropy is defined as the amount of disorganization of something or the degree of disorder in any system. The entropy of things tends to be lower if they are nicely packed together and increase when the things are loosely packed (Xavier, 2014).

Jacob Bekenstein also raised one question as he said that according to second law of thermodynamics, if the black hole has an entropy, it must also have a temperature and it has a temperature then it must radiate the heat to the environment, but if nothing can escape from the black hole then how will heat be radiated and if it does not radiate, t violates the second law of thermodynamics.

This statement from a young student was a challenge to the idea of Hawking and in the efforts to prove him wrong, Hawking started searching for entropy. He even embraces the advice from other scientists but every one of them stated that if a black hole has entropy it must radiate energy. 

Challenge to Hawking's Idea

Hawking realized there is another concept in physic called quantum mechanics which tells about the working principles of vacuum (Susskind, 2014). According to quantum physics, space is never empty, particles are being regularly created and destroyed in the vacuum and the particles do this on the basis of Heisenberg’s uncertainty principle.

The empty space is not really empty but it contained virtual particles known as matter and antimatter. These pair of particles came into existence for a very small during of time and annihilates each other very quickly (Blundell, 2015).

Hawking realized that if the same phenomenon occurs near the event horizon, it is possible that one of the virtual particles will fall into the black hole and the others will escape becoming a real particle and therefore black hole will lose its energy.

Delaney further explained that these particles which form simultaneously in the vacuum can be assumed as electrons and photons. If they make contact with each other they disappear giving away little energy but near the event horizon of a black hole one of the particles zips off into space and the other gets drawn inside the black hole. The particle that zips away to the universe carries away a little energy (Ngampitipan, 2014).

“In the process a black hole is actually sort of radiating away a little bit of energy in this pair production process, meaning that it is quietly and steadily evaporating but it takes billions of year for a black hole to completely disappear,” Professor Delaney said.

While starting, this process occurs extremely slowly but as a black hole gets smaller and smaller, the process starts to gain the speed because the temperature of smaller holes is much high than that of massive black holes and if the temperature is high its radiation emission is also high (Calmet, 2013).

“it is believed that when a black hole becomes very small and enters the last stage of its life, it dies with a huge explosion which radiates the energy equal to the billions of nuclear bombs and this marks the death of a black hole,” said Professor Peet.

This theory was of importance from the point of view of fundamental physics because for the first time the idea of Quantum Mechanics was joined with the Theory of General Relativity and it is one of the greatest unsolved problems in physics that helps to bring the theory of gravity into an overall understanding of Quantum Mechanics and it was one of the steps toward the “Theory of Everything”.

“I think that 20th century had two principal scientists, Stephen Hawking and Einstein," said Professor Delaney. "The two of them were able to make a great deal of sense of the universe which is quite confusing for most of us. They were able to check observation, theories and marry them together in ways that few scientists were able to do (Bailyn, 2014). Stephen achieved this with the added disadvantage of his illness and that what makes his ability to do the things that he did even more astonishing,” he added.

The material to be added, I will add some more scientific statements from Hawking. He will be elaborating more on black holes. Apart from that, I wish to do more elaborate and extensive research on black holes from sources that are different from those authored by Hawking.

References

Bailyn, C. D. (2014). What Does a Black Hole Look Like? New York: Princeton University Press.

Blundell, K. (2015). Black Holes: A Very Short Introduction. Oxford: Oxford University Press.

Calmet, X. (2013). Quantum Black Holes. Kansas: Springer Science & Business Media.

Hawking, S. (2016). Black Holes. New York: Random House Publishing Group.

Ngampitipan, T. (2014). Rigorous Bounds on Greybody Factors for Various Types of Black Holes. Salt Lake: Chulalongkorn University.

Ong, Y. C. (2015). Evolution of Black Holes in Anti-de Sitter Spacetime and the Firewall Controversy. Beijing: Springer.

Susskind, L. (2014). The Black Hole War: My Battle with Stephen Hawking to Make the World Safe for Quantum Mechanic. London: Little, Brown.

Xavier, C. (2014). Quantum Aspects of Black Holes. Salt Lake: Springer.

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