17th Dimension

Hawking radiation is often intuitively visualized as particles that have been through (barrier) horizon. However, it is not clear where the barrier that must be breached. The key is to implement the conservation of energy, so the black hole contracts during the radiation process.

A direct consequence is a spectrum of radiation can not be entirely thermal. Amendments to the thermal spectrum is expected from the characteristic shape keuniteran quantum theory. This may just may be a clue to the puzzle of information black hole.

Classically, a black hole is an absolute jail, all that goes into it must be locked, there's no way out. Furthermore, because no one can come out, a classical black hole can only grow 'big' as time passes.

Then, at the time, was a shock to physicists as Hawking showed that quantum mechanics can actually be a black hole radiates particles. With the issuance of this Hawking radiation, black holes can lose energy, shrink, and then eventually evaporate completely.

How can this happen? When an object which is classically stable (fixed energy, no change) into a quantum mechanics becomes unstable (no change), then naturally we would expect that there is a breakthrough barrier (tunneling).

Clearly, when it was first proved the existence of Hawking radiation of black holes, he described it as a breakthrough barrier triggered by vacuum fluctuations (the appearance of particles and antiparticles of the combined system with initial energy = zero, vacuum) in the near horizon. Previously, the horizon is the bulkhead between the 'in' and 'outside' the black hole where light can not get out of him.

Therefore, we call these black holes are 'black' because there is no information (classically) that arrive at the observer.

Hawking's idea is right around the pair production event horizon, inside or outside. Particles with positive energy created by pair production in the horizon will break through the barrier horizon - though no klask trajectories are possible, but this can be allowed quantum. In this case we can imagine antiparticle (negative energy) that remains in the horizon of a black hole resulting in the total energy decreases.

Then, if the right pair production occurs outside the horizon, then antipartikelnya that comes into the horizon, and we can imagine the effect is the same as before. There are particles that 'run' away from the black hole (this is the radiation) and the resulting energy (mass) black hole is reduced.

But unfortunately, although the picture of Hawking as described above, but the original reduction was not initially take advantage of this picture is complete. It's quite odd.


 To take full advantage of this picture, we need to solve 2 problems: One is technical, to conduct breakthrough calculations barrier, it takes a well-behaved coordinate system on the horizon (no infinity). Second: Conceptually, what barriers must be breached?

Usually, when the barrier breakthrough occurs, there are two separate areas which combined classic by a trajectory in imaginary time / complex.

In the WKB limit (a term approximation in quantum), the opportunity to break through barrier associated with the imaginary part of the action (particle) when passing through a classically forbidden trajectory with the expression

    G μ exp (-2 Im S)

with S is the action on the related trajectory. But the problem arises when this technique is used for black holes. Apparently, the 'outside' and 'in' this horizon zero cm apart in distance. Tell a separate pair of particles produced by infinitesimal beyond the horizon, but he still can 'run'. How can this happen?

As Hawking initially described, that particles break through the horizon, this is indeed happening. But his explanation to the argument that a little complicated, because there is no barrier which had previously been there (been there By design).

However, what happens is that particles break through the barrier he created his own (remember the relativity, the motion of objects is determined by the surrounding geometry, this geometry is determined by the content of the mass and angular momentum of the black hole). The most important point that energy must be conserved. When the radiation occurs, the energy / mass black hole decreases, the more he shrank.

This shrinkage effect on the small radius of the black hole. The size of the contractions that occur naturally depend on the number of particles of energy that comes out. The bigger the energy out, the greater the contraction also occurs. Here it will be seen that the particles that come out that is what defines the barrier. But we will see this more clearly in the next section.

More details of course we really need a complete theory of quantum gravity here (which is still far from final). Tell the generally accepted point of view, we need to involve graviton (gauge fields that mediate interactions in quantum gravity, such as photons for quantum electromagnetic interaction).

But as we discuss the symmetry of black hole systems the ball, then no analysis is required graviton which has spin 2, because then the ball would not algi symmetry. All it takes is parikel spin zero (scalar) so that the degrees of freedom which will be discussed only when there was breakthrough parikel position barrier.

Armed with this view, we can do the calculations to break through the barrier in the Hawking radiation. Coordinates are used just as it certainly is not a standard like Schwarschild, because in these coordinates the horizon is not of good character, there is lack berhinggaan for spatial sector radius, dr.

But with the transformation of Painleve (which finds a transformation as a critique of general relativity in which the singularity can be removed only with a trasnformasi coordinates). Line element due to this transformation to the original geometry is Schwarschild

DS2 =- (1-2M / r) dt2 +2. sqrt (2M / r) + dr2 + r2dX2 dtdr

with the DX2 is the metric for 2-dimensional ball.

With this line element, we can calculate the safe integral of the particle action (p.dr with p = momentum and dr = infinitesimal radius). The integration radius is the horizon radius at first, until the particles have come out, with energy E, ie from r = 2M to r = 2 (ME).


Integral is analogous to the integral calculation of the probability of normal barrier breakthrough. It is clear that the barrier in the Hawking radiation depend on the particle energy out, as has been alluded to earlier.

By equating exp (-2 Im S), the calculation of the Boltzmann factor, exp (E / T) with T = temperature of Hawking, Hawking temperature, it can be found such that at first found first.