Hawking radiation

The Hawking radiation is a 1975 postulated by the British physicist Stephen Hawking radiation of black holes. It is derived from concepts of quantum field theory and general relativity.

The Hawking radiation is also used for the current research of interest because they could serve as a potential testing ground for a quantum theory of gravity.

Descriptive interpretation

In contrast to classical physics, the vacuum in quantum electrodynamics is no " empty nothing " but a complicated structure of vacuum fluctuations. These vacuum fluctuations consist of virtual particle-antiparticle pairs that exist according to the quantum mechanical uncertainty principle only for a short time. These pairs can be both massive and massless particles such as photons. Generation and destruction of virtual particles also takes place in the vicinity of the event horizon of black holes. Here, first we get virtual particle-antiparticle pairs, due to the energy conservation has one partner and the other partner negative positive energy. In this case, a virtual particle with negative energy can fall into the black hole. Thus, the two partners are separated by the event horizon. The one partner falls into the black hole, while the second partner can escape as a real particle in free space. The collapsing into particles with negative energy thereby releasing as much potential energy as is needed for pairing and the catapult the other particle in the gravitational field. " According to Einstein's equation E = mc ², the energy of the mass is proportional. Flows negative energy into the black hole, as a result, reduces its mass. "

Those particles that escape the black hole as a real particles forming the Hawking radiation. For large black holes, the particles are almost exclusively low-energy photons.

Since the vacuum fluctuations are favored by a strong curvature of space- time, this effect is particularly important in low-mass black holes. Black holes are of low mass, low expansion ( Schwarzschild radius ), its event horizon and the surrounding space-time are correspondingly more strongly curved. The larger and thus more massive a black hole is, the less it radiates so. The smaller the black hole, the faster it evaporates.

Spectrum and size dependence

Since the strength of the gravitational field in the interior of the black hole increases further with decreasing distance to the center of the black hole, the track is getting shorter, must travel a virtual particle with negative energy, until it becomes a real particle. The emission rate for particles and thus the apparent temperature of the black hole thus increases with decreasing mass of the black hole. The associated Hawking radiation, there would probably just have the spectrum of a black body.

Large black holes as they arise from supernovae, have such a low level of radiation that it is not detectable in the universe. Small black holes have, however, according to this theory, a significant heat radiation, which means that its mass decreases rapidly. Thus, a black hole of mass 1012 kg - the mass of a mountain - a temperature of about 1011 Kelvin, so that in addition to photons also prone mass particles such as electrons and positrons are emitted. Thus, the radiation is continuing to grow, so that such a small black hole in a relatively short time completely evaporates ( vaporizes ). Decreases the mass of less than 1000 tons, so the black hole explodes with the energy of several million Mega, or Teratonnen TNT equivalent. The lifetime of a black hole is proportional to the cube of its original mass. The lifetime of a black hole with the mass of our Sun has 1064 years. This puts it beyond all limits observation.

The Hawking radiation is a violation of the second law of black hole dynamics, since the radiation mass - and thus the surface horizon - the black hole decreases. However, at the same time a corresponding amount of entropy in the form of radiation is emitted, suggesting a deeper relationship between the two variables.

Hawking temperature

Means of Hawking entropy and the thermodynamic definition of the temperature T

Where S is the entropy and E is the energy that can be a black hole assign a radiation temperature, which is also known as the Hawking temperature TH and is given by:

Where ħ the reduced Planck constant, c is the speed of light, G is the gravitational constant, M is the mass of the black hole and kB is the Boltzmann constant.

This equation is based on approximation of the thermodynamic equilibrium. A part of the generated radiation is scattered back by the gravitational field of the black hole. Black holes are therefore rather than " gray bodies " to understand a relation to the model of the black body radiation intensity decreased. The approximations in the derivation are only valid for black holes of large mass, since it was assumed that the curvature of the event horizon is negligibly small, so that " ordinary " quantum mechanics can be operated in the Rindler space-time. For very small black holes, the intensity distribution should differ significantly from that of a black body, because in this case the quantum mechanical effects are so dominant that the semiclassical approximation is no longer valid.

The Hawking effect represents a special case of the Gibbons - Hawking effect

Hawking entropy and generalized second law

By the entropy equation of Hawking, a correlation between thermodynamics, quantum mechanics, relativity theory and classical mechanics can be produced:

The derivation of this equation using the Stefan- Boltzmann law.

This leads to the so-called " generalized second law of thermodynamics ". The second law of thermodynamics states that the entropy of a system can not decrease with time. The generalization states that the sum of " ordinary" Entropy and the total area of ​​event horizons can not decrease with time.

Application: merging and decaying black holes

Consider the merger of two black holes of masses M1 and M2. The fusion process is isentropic, that is, the ordinary entropy of the system does not change. Since the area of the event horizon area A is proportional to the square of the mass, the result for the change:

Thus, the total area increases and the merger of two black holes is thus not in conflict with the generalized second law.

Consider now the decay of a black hole of mass M1 M2 into two smaller black holes of masses M1 and M2. The Zerfallssprozess is isentropic again. Then for the change in the total area of ​​the event horizons:

The total area would therefore decrease in the decay of a black hole into two smaller ones. The generalized second law of thermodynamics thus forbids the decay of a black hole into two smaller ones.

Conclusions and Outlook

The prediction of Hawking radiation is based on the combination of effects of quantum mechanics and general relativity and thermodynamics. Since the unification of these theories has not yet been ( quantum theory of gravity ), such predictions are always fraught with uncertainty.

With the thermal radiation of the black hole loses energy and mass. It thus " shrink " with time. Assuming a blackbody spectrum, as well as a Boltzmann law for the intensity, so can a radiated power and derive from it a lifetime for a black hole is proportional to the third power of the mass:

However, black holes stellar origin have a lower temperature than the cosmic background radiation, which is why these black holes absorb thermal energy from their environment because of their large mass. In this case, no shrinkage of the black hole is possible because by the inclusion of radiation energy, the mass in this case increases according to the Einstein's mass-energy equivalence formula. Only when the ambient temperature drops below the temperature of the black hole, the hole loses by radiation emission to ground. For black holes laws can be derived, which are largely analogous to the three main sets of classical thermodynamics. Heuristic considerations led JD Bekenstein in 1973 to the hypothesis that the surface of the event horizon could be a measure of the entropy of a black hole. Can with the entropy and the temperature define a ( generalized ) are placed second law of thermodynamics for black holes.

What's happening "at the end of its life, " a black hole at the still unclear. In particular, there arises the so-called information paradox. It is the question of what happens at the " evaporation " of the black hole with the original information that is plunged in its formation into the black hole and, according to certain claims arising from the quantum mechanics can not be lost.