Black Holes - A Closer look at Hawking Radiation

Stephen DiIorio | Physics 123 | Fall 2012 | Union College

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Hawking Radiation
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Stephen Hawking Had the Answer! Sort of . . .

To tackle all of the problems created when we look at the thermodynamic side of black holes, Stephen Hawking considered the quantum-mechanical processes that take place near a black hole. In classical mechanics, we think of space as just being empty; nothing interesting happens, and nothing, that we are aware of, fills the void. However, modern physics ignores this and says that in this vacuum the creation and destruction of particles and antiparticles occur everywhere all the time. The creation and destruction of these particle-antiparticle pairs is considered to be "virtual" because if they were real or permanent, it would violate the conservation of energy and momentum. So long as they exist for a short enough period of time (determined by Heisenberg's uncertainty principle where the amount of time allowed is Δt > h/2mc2) they are theorized to exist. [4]

If we consider these virtual processes to occur near the event horizon of a black hole, which Hawking did, we would not expect to see immediate destruction as predicted by our model. Imagine this process happens extremely close to the event horizon of a black hole. As soon as these particles come in to existence they would both experience drastically different gravitational forces due to the sharp gradient of tidal forces caused by being so close to the black hole. One particle will accelerate towards the black hole giving the other a chance to escape and radiate out in to space. The black hole used some of its gravitational energy to produce these two particles, so it loses some of its mass if a particle escapes. This happens often enough that black holes evaporate over time. The rate at which these black holes is as follows:

Time for Black Holes to Evaporate
. This means that black holes evaporate fairly slowly when they are first born, but as they die out and reach the end of their life, they evaporate in a burst of gamma radiation. It is calculated that stellar-massed black holes take only 13 billion years to evaporate, so those created near the beginning of the universe should die soon and be detectable. [5]

Stephen Hawking
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Leonard Susskind
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Hawking may have tackled one issue, but he created several more; one of the biggest problems with this radiation is that, on its surface, it implies that information is lost (something that can never occur within our physical world). Nothing else in the universe breaks this fundamental conservation of information. Even detonating a nuclear weapon does not destroy any information. It may scramble everything near it, but if we could, we would still be able to watch and observe the locations and states of every particle and retrace their steps. Hawking believed that radiated particles shared no information or connection to the particles that entered the black hole. Because the radiated particles had no physical connection the particles at the center of the black hole, the particles were independent from one another. This problem caused an uproar in physics that quickly became known as the Black Hole War. [3]

After proposing this, Stephen Hawking was quickly thrown in a debate with another rising physicist named Leonard Susskind. Hawking stuck with his calculations, but Susskind was able to come up with a solution that saved physics and ended this debate. Susskind showed that there was a connection between the matter at the center of the black hole and the matter at its surface. Known as the holographic principle, part of the larger string theory, Susskind showed that the surface of a black hole was a 2D representation of the 3D center of a black hole. All of the information in the center of a black hole could be seen on its surface. With this, Susskind showed that no information was lost inside a black hole. Hawking admitted defeat in this debate and this loss of information was resolved. [3]

So what does Hawking Radiation and the Holographic Principle solve? These two achievments mean that the problems created with Bekenstein's model are no longer a problem. Hawking radiation gives us the radiation we were looking for in an object that has a temperature. Black holes have been shown to now emit particles with a distribution of thermal energy. Hawking figured out that this distribution for non-rotating black holes was,

Temperature of Black Hole
. Similarly, the Holographic principle made the information inaccessible inside the black hole accessible. The surface of the black hole now served as a means of storing all of the information, the microstates like the rotational and vibrational energies of all the atoms etc. It was this synthesis of both our classical model and quantum mechanics that led to a solution and thermodynamic description of blakc holes.

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Last Updated November 12, 2012