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Black Hole Theory & Hawking Radiation

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The simplest type of black hole, in which the core does not rotate and just has a singularity and an event horizon, is known as a Schwarzschild black hole after the German physicist Karl Schwarzschild who pioneered much of the very early theory behind black holes in the 1910s, along with Albert Einstein. In 1958, David Finkelstein published a paper, based on Einstein and Schwarzschild’s work, describing the idea of a “one-way membrane” which triggered a renewed interest in black hole theory (although the phrase itself was not coined until a lecture by John Wheeler in 1967).

In 1963, the New Zealander Roy Kerr discovered a solution to Einstein’s field equations of general relativity which described a spinning object, and suggested that anything which collapsed would eventually settle down into a spinning black hole. It spins because the star from which it formed was spinning, and it is now thought that this is actually likely to be the most common form in nature. A rotating black hole would bulge outward near its equator due to its rotation (the faster the spin, the more the bulge).

Spinning and non-spinning black holes - click for larger version
(Click for a larger version)
Spinning and non-spinning black holes
(Source: Chandra X-Ray Observatory:

In the mid-1960s, the young English mathematician Roger Penrose devoted himself to the study of black holes and, in 1965, he proved an important theorem which showed that a gravitational collapse of a large dying star must result in a singularity, where space-time cannot be continued and classical general relativity breaks down. Penrose and Wheeler went on to prove that any non-rotating star, however complicated its initial shape and internal structure, would end up after gravitational collapse as a perfectly spherical black hole, whose size would depend solely on its mass.

In the late 1960s, Penrose collaborated with his Cambridge friend and colleague, Stephen Hawking, in more investigations into the subject. They applied a new, complex mathematical model derived from Einstein's theory of general relativity, which led, in 1970, to Hawking's proof of the first of several singularity theorems. Such theorems provided a set of sufficient conditions for the existence of a gravitational singularity in space-time, and showed that, far from being mathematical curiosities which appear only in special cases, singularities are actually a fairly generic feature of general relativity.

Although it may seem a very complex, peculiar and perhaps counter-intuitive object, a black hole can essentially be described by just three quantities: how much mass went into it, how fast it is spinning (its angular momentum) and its electrical charge. This came to be known as the “No Hair Theorem”, after John Wheeler’s comment that “black holes have no hair”, by which he meant that any other information about the matter which formed a black hole (for which "hair" is a metaphor) remains permanently inaccessible to external observers within its event horizon, and is all but irrelevant.

Brandon Carter and Stephen Hawking proved the No-Hair Theorem mathematically in the early 1970s, showing that the size and shape of a rotating black hole would depend only on its mass and rate of rotation, and not on the nature of the body that collapsed to form it. They also proposed four laws of black hole mechanics, analogous to the laws of thermodynamics, by relating mass to energy, area to entropy, and surface gravity to temperature.

Hawking radiation as particle pairs are created near a black hole - click for larger version
(Click for a larger version)
Hawking radiation as particle pairs are created near a black hole
(Source: University of St Andrews:

In 1974, Hawking shocked the physics world by showing that black holes should in fact thermally create and emit sub-atomic particles, known today as Hawking radiation, until they exhaust their energy and evaporate completely. According to this theory, black holes are not completely black, and neither do they last forever.

Hawking showed how the strong gravitational field around a black hole can affect the production of matching pairs of particles and anti-particles, as is happening all the time in apparently empty space according to quantum theory. If the particles are created just outside the event horizon of a black hole, then it is possible that the positive member of the pair (say, an electron) may escape - observed as thermal radiation emitting from the black hole - while the negative particle (say, a positron, with its negative energy and negative mass) may fall back into the black hole, and in this way the black hole would gradually lose mass. This was perhaps one of the first ever examples of a theory which synthesized, at least to some extent, quantum mechanics and general relativity.

A corollary of this, though, is the so-called “Information Paradox” or “Hawking Paradox”, whereby physical information (which roughly means the distinct identity and properties of particles going into a black hole) appears to be completely lost to the universe, in contravention of the accepted laws of physics (sometimes referred to as the "law of conservation of information"). Hawking vigorously defended this paradox against the arguments of Leonard Susskind and others for almost thirty years, until he famously retracted his claim in 2004, effectively conceding defeat to Susskind in what had become known as the "black hole war". Hawking's latest line of reasoning is that the information is in fact conserved, although perhaps not in our observable universe but in other parallel universes in the multiverse as a whole.

Unfortunately, Susskind's proposed solution is even more difficult, and almost impossible to envisage or explain in an understandable way. He suggests that, as an object falls into a black hole, a copy of the information that makes it up is sort of scrambled and smeared in two dimensions around the edge of the black hole. Furthermore, Susskind believes that a similar process occurs in the universe as a whole, which raises the rather alarming idea that what we think of as three-dimensional reality is in fact something like a holographic representation of a "real" reality, which is actually contained in two dimensions around the edge of the universe.

It is also theoretically possible that "primordial" or "mini" black holes could have been created in the conditions during the early moments after the Big Bang, possibly in huge numbers. No such mini black holes have ever been observed, however - indeed, they would be extremely difficult to spot - and they remain largely speculative. It is anyway likely that all but the largest of them would have already evaporated by now as they leak away Hawking radiation. According to Hawking's theory, the amount of mass lost is greater for small black holes, and so quantum-sized black holes would evaporate over very short time-scales. But it is hoped that such mini black holes might be experimentally re-created in the extreme conditions of the Large Hadron Collider at CERN, which, among other things, would lend much-needed credence to some of the current theoretical predictions of superstring theory regarding gravity.

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