The thermodynamics of a black hole
Quantum field theory
The simplest way to understand the mechanism of Hawking radiation is through quantum field theory (QFT). In physics, quantum mechanics (QM) is the field that studies the incredibly small while QFT is a subtopic of QM and attempts to explain objects that move at speeds near c at a quantum/subatomic level (Miller, 2018). It is important to note that, as QFT is a subtopic of QM, gravity cannot be included in this model. Gravity should not be seen as a force that is composed of particles that mediate attraction, but rather as the warping of space-time (Weinberg, 1997). As a result, any model of space-time that is a QFT cannot include gravity. QM explains how in a vacuum region of space, particles are constantly popping into and out of existence (quantum fluctuations) – often referred to as virtual particles. Thinking about wave-particle duality, 5 instead of considering particles like small spheres, they should be thought of as waves or strings. If a string suspended between two walls is plucked, it will vibrate up and down. If a point on a string were pinched while vibrating, that point would not be able to move up and down (PBS Space- time, 2018).
Destructive interference (Uccon, 2020)
In the context of QFT, black holes do something similar. Instead of thinking of virtual particles as spherical objects, think of them as 2 waves (wave-particle duality), one with positive mode and one with a negative mode. These opposite modes will cancel each other out but at the event horizon of a black hole this does not happen. Like a finger pinching the string, the black holes prevent some of the cancellation from occurring, thus the modes do not cancel each other.
The following section will breakdown what exactly a black hole is, the properties that it possesses and how Hawking radiation emerges.
1.1
Black holes
In Schwarzschild’s published solution to Einstein’s field equations, he formulated a metric that perfectly described a black hole with no charge or angular momentum and only mass. This type of black hole is surrounded by a spherical region called the event horizon, which is positioned at the Schwarzschild radius. The event horizon is the point in which the escape velocity is c, hence it is the point of no return (Michael, 2004).
1.2
Hawking radiation in quantum field theory
Previously I presented an analogy of how black holes behave in everyday scenarios. A black hole is the finger that pinches the string, prohibiting the cancellation of opposite frequencies (annihilation). As these modes do not cancel, the black hole has turned a vacuum into a particle-filled region of space. The key principle is that these created modes (now called particles) need energy to suddenly appear and
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