Black Holes: #2 Glowing and Shrinking

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Today we follow on from the first in the series on Black Holes (#1 Falling In) and talk about how black holes aren’t thought to be that black after all with the idea of Hawking Radiation. The post will then cover how, as a result of this radiation black holes are thought to evaporate and as a result shrink! This topic is logically chosen as the next in the series on black holes due to the appearance of antimatter in the theory and our recent blog post, ‘What’s the matter with antimatter?’ Perhaps take a quick read of that before you move onto the below, it’s only a short one. I hope to keep this post fairly light as well so for all you black hole experts out there, forgive my simplifications at times.

A black hole can be described in its full glory by three quantities alone: mass, angular momentum (how fast it spins) and electrical charge. The fact that any other information about what formed the black hole is redundant is known as the ‘No Hair Theorem.’ Hawking went on to show that the size and shape of a spinning black hole would depend on those three quantities alone. At this time some further laws of black hole mechanics were also settled, collectively known as black hole thermodynamics: the mass of a black hole is related to its energy, the area of a black hole is related to its entropy and the surface gravity of a black hole is related to its temperature.

With that out the way, onto the good stuff… Hawking radiation is Hawking’s theory that a Black Hole emits energy in the form of radiation until it exhausts its energy supply. Remember due to Einstein’s infamous equation E = mc²; energy and mass are proportional therefore a loss in energy is equivalent to a loss in mass. So as the Black Hole spews out energy it looses mass, gradually becoming smaller and smaller until it effectively ‘pops’. This is known as ‘Black Hole Evaporation’. But wait, wasn’t it the case that nothing could escape a black hole?! How is this energy suddenly being spewed out and where does it come from?! What is this mysterious Hawking radiation made of? To this we must turn back to quantum mechanics, antiparticles and uncertainty.

A wise man called Werner Heisenberg in 1927 postulated Heisenberg’s uncertainty principle. The uncertainty principle asserts a fundamental limit to the precision with which a certain pair of physical properties of a particle can be known. There are two of these expressions – one for position (x) and momentum (p) and another for energy (E) and time (t).

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The first says a particles position and momentum cannot be known simultaneously beyond a certain precision –  for a fixed position there is a unknown range the momentum can assume. This range is shown by the triangle symbol (greek letter delta), which effectively means ‘change in’. Likewise, over a fixed time there is an unknown range the energy can assume. These effects come into play on very small length scales which is what the h represents in the equation. When a mass is very large, the uncertainties become very small and classical physics is applicable. As such these phenomena are only noticeable in the quantum world. So in quantum physics, in a moment there can be a change in the amount of energy at a point in space. This is known as a quantum fluctuation. Energy can temporarily appear in what was, previously empty space (empty space is often referred to as a vacuum).

You may be thinking, hang on everything I know is going out the window now – what happened to energy always being conserved?! But i’m afraid you’ll have trust me for now when I say the wacky world of the Quantum realm allows this with peculiar behaviour of quantum superpositions of particle states when at the lowest-energy levels (i.e. the vacuum state/empty space). Suffice it to say the violation is allowed and I might ask Joe, the resident master on Quantum behaviour here at RTU, to do a post on it in the future. Anyhow, this energy can manifest itself in the form of energetic particles, and in order to conserve quantum properties like charge, spin etc these energetic particles are produced as particle-antiparticle pairs. The pairs are known as ‘virtual particles’ because they often pop out of existence as soon as they created.

Strange things happen when these fluctuations occur near the horizon of the Black Hole. [For a recap on what the horizon is in detail see Black Holes #1, but in brief: the event horizon is the distance from the centre of the black hole from which nothing can escape due to the immense gravitational tug of the black hole]. If a fluctuation creates a particle, anti-particle pair just outside the black hole event horizon, the gravitational energy of the black hole can ‘boost’ these particles into becoming real particles. Then the funny thing happens… Hawking predicts that one of the particles is sucked into the black hole, past the horizon, while the other particle escapes.

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Because nobody can see past the horizon, it appears as though matter/radiation/energy (all the same thing at the end of the day) is being spewed out of the black hole. Instead of the being void of all life, the horizon is actually hub of activity, with exchanges like this going on all around the perimeter. Through spewing out the particles energy is given off and the black hole is not black after all, in fact it glows with this radiation emission. 

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Now here’s the final jump, seeing as the energy and mass have been shown to be equivalent from Einstein’s E=mc², and the creation of the particle pair came from the gravitational energy of the black hole itself, if one of the particles escapes to the outside world, the black hole will loose energy or – loose mass. But you might think, what about the particle that was swallowed, surely this adds to its mass to counteract the loss. Things get a little fiddly here, we’re nearly at the end, bear with me if you can…

Since the particle that is emitted has a positive energy, the particle that get absorbed by the black hole must have a negative energy, relative to the outside universe – in order to preserve the laws of thermodynamics (conversation of energy). We must not confuse the particle and antiparticle as being the positive energy and negative energy particle. Popular accounts of Hawking radiation explain the process as it being the antiparticle that is always absorbed, this is not the case. It is a 50/50 chance that either it will be the particle or the antiparticle that is the unlucky partner that gets sucked in but in order to preserve the law of thermodynamics the absorbed particle is assigned negative energy.

Ultimately, the particle that gets spewed out, is a product of the energy fluctuation of the black hole and as such we now have a particle, bobbing freely around the universe, that we never would have had before without the black hole. In a sentence: the black hole suffers a net energy loss due to this phenomena, therefore a net mass loss as it radiates away particles, meaning it gets smaller and shrinks. Shrinks and shrinks until it eventually disappears all together. The complete description of the dissolution requires a model of quantum gravity but it is hoped that tiny black holes might be experimentally re-created in extreme conditions at CERN in the future! So there we have it, black holes… not so black or devoid of life after all, according to Hawking. In fact, fantastical beasts which continually glow and over time shrink as they leak away Hawking radiation until they cease to exist all together. A pretty cool life for the elderly years of a massive star if Hawking is correct.

 

 

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