The thermodynamics of a black hole
Kamran Din
What is a black hole and the information paradox?
A black hole is an object in space that has such a powerful gravitational field, not even light can escape (Hawking, 1998). While black holes were first theorized as an object of science fiction, their existence was proved but created discord due to their obscure nature. In 1974 Cambridge physicist Stephen Hawking proposed a process by which black holes lose mass, Hawking radiation, contradictory to previous understanding. He published these findings in his paper ‘Black hole explosions?’ (Hawking, 1974). This loss of mass from black holes is problematic, as it creates several paradoxes, but for the purpose of this dissertation I will be evaluating the information paradox . To break down the paradox, this dissertation will thoroughly examine all the background knowledge, ranging from quantum mechanics to relativity, required to understand this topic. Following the introduction, this dissertation will then explore the mechanism behind the information paradox , and how this develops into the holographic universe .
Relativity
At the beginning of the 20 th century, German-born physicist Albert Einstein developed a theory of relativity to explain the behaviour of everyday/classical objects. This thesis can be further subdivided into two theories, general and special relativity. Special relativity, published in Einstein's miracle year, 1905, states that the laws of physics remained the same for all moving bodies. While special relativity is incredibly complex, it can be summarized very briefly. If an object had an escape velocity 2 (velocity required to overcome gravitational field of body) greater than c , nothing could ever leave that body. Such objects were theoriz ed as ‘ b lack’ stars, and because of this law of equivalence, there is no return from such a body. From certain philosophical viewpoints, such objects cannot be regarded as part of our universe. General relativity, published shortly after special relativity, explains the behaviour of gravity, not how it acts as a force, but how it curves space-time (Walter, 2000). General relativity was beautifully summarized by John Wheeler: ‘ Space-time tells matter how to move; matter tells space-time how to curve ’ ( NewScientist , 2021). In essence, general relativity explores how mass affects the curvature of space-time.
To visualize what a black hole looks like, general relativity can be applied in the context of space-time. For example, the universe could be imagined as a flat piece of paper, analogous to the surface of a trampoline. If a bowling ball is placed on the surface, the surface would bend in this region but remain flat in the other regions. This is equivalent to putting a star or a planet in the universe. Now if the density of that bowling ball is increased, this curvature will become even greater, and the slope will become deeper until nothing can escape from that hole – a black hole.
Diagram of curvature of Space-time (European Space Agency, 2015)
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