# Hawking radiation can be used for anything

## Hawking radiation

To put it briefly: The classical black holes as a solution to Einstein's General Theory of Relativity (GTR) are absolutely black at the event horizon. English astrophysicist *Stephen W. Hawking* took into account quantum effects in the vicinity of black holes in a calculation in 1974 and found out that particles would then arise at the event horizon which also left the area of influence of the hole. These particles are subsumed under the term*Hawking radiation* or *Hawking emission*. It is a purely theoretical work, and this one *Hawking effect* could so far **not confirmed experimentally** become.

### Role of the event horizon

Hawking radiation is difficult to detect because of the following: Hawking radiation is very low in intensity, and candidates for black holes are at astronomical distances. Other radiation effects in the vicinity of the hole, especially the glowing accretion flow, clearly outweigh the Hawking effect - should it exist. Hawking radiation is tied to the existence of the event horizon. If there is no horizon, then there is no Hawking emission either (but presumably another form of thermal emission). Meanwhile, theorists have proposed alternative models to the black hole that do not have a horizon. If the Hawking effect is not observed, it gives these alternatives slightly more weight - but research in this area is not complete. The spacetimes without a horizon are called gravastars and holostars.

### What was Hawking doing exactly?

If you go into the details of this effect, it becomes relatively complicated - also linguistically - as the following explanations will show. A mathematical derivation requires knowledge of GTR and quantum field theory. As anticipated, Hawking radiation is not a phenomenon of the classical theory of relativity, but a **Quantum effect**. In the context of thermodynamics and quantum field theory (QFT), Hawking went beyond the concepts of classical black hole theory and made one *semiclassical approach*by examining quantum fields on the background of curved spacetime. The fields associated with particles such as electrons, photons or neutrinos are quantized, **Not** however the gravitational fields. They are, however, described with the GTR. In this sense, Hawking's approach is a semiclassical quantum gravity concept. It must be emphasized that he failed to quantize gravity.

The consequences of this treatment are astonishing: while in the classical theory black holes are pure absorbers of particles because they disappear 'behind' the event horizon, the quantum field theoretical approach opens up the possibility that black holes also emit particles at a constant rate **Hawking radiation**. It should be noted that the term *radiation* does not necessarily mean pure electromagnetic emission, but generally all possible particles. In the following it is outlined in the language of theoretical physics (unfortunately there are no adequate alternatives) how this happens:

### ... and in the mathematical-physical way of speaking?

The particles are described as in quantum field theory as **scalar field operators**who the *canonical commutator relations* fulfill. The Klein-Gordon equation is then generalized to curved metrics by replacing ordinary derivatives with covariant derivatives. For the sake of simplicity, consider massless scalar particles. The solutions of **covariant Klein-Gordon equation** have the familiar form with creation and annihilation operators and enable the definition of a vacuum state. The theory of relativity allows this state to be viewed in different orthonormal bases, because the hypersurfaces that can be selected within the framework of the ADM formalism are equal to each other. With two arbitrarily chosen orthonormal bases one defines oneself in this way **different vacuums** with different annihilation operators. From one base you can go to the other via the *Bogoliubov transformations* switch. If you now form the **Vacuum expectation value** for an occupation number operator, based on the different vacuums, one finds that it becomes finite. He's not going away! The definition of a vacuum state is ambiguous in the theory of relativity and depends on the observer. That ultimately means that the **Particle term relative** is: in one reference system the vacuum appears filled with real particles, in the other it looks like a vacuum that is filled with virtual particles. Both observers are right!

However, one can compare the vacuum expectation values if one assumes a curved spacetime that is asymptotically flat in the past and future. That is, the metrics that satisfy the covariant Klein-Gordon equation vanish at infinite intervals. This balance shows that **the gravitational field creates particles** what is called Hawking radiation!

### All right! Now please for people like you and me

After this abstract explanation, there now follow two clear interpretation possibilities that are equivalent to each other: The first is based on the quantum field theoretical concept of a quantum vacuum described above. The second is more of a classic nature and uses the concepts of thermodynamics.

**(1)**According to the quantum theory, the whole space, including the vacuum, is filled with**Pairing of virtual particles**and their antiparticles (see antimatter). Their energy is so high that the particles within the framework of Heisenberg's uncertainty relation (position-momentum uncertainty, energy-time uncertainty) have a very short lifespan and therefore cannot be measured. In this sense they are called*virtual*. Constantly annihilate, i.e. these particles with their corresponding antiparticles annihilate in electromagnetic radiation (virtual photons) and form anew in pairs. The quantum vacuum is therefore not a quiet place, but a complex structure that is populated by virtual particles. [*As an aside*: This phenomenon is indirectly related to the**Lamb shift**, a shift of the spectral lines, measurable in the hydrogen spectrum. This means that the concept of virtual particle pairs is not a hypothesis, but a fact that has been verified in an experiment!]

If such a pair materializes near the event horizon of a black hole, it is possible that one of the particles falls into the black hole while the other escapes to infinity (see figure on the right, red pair of particles). This separation can be brought about, for example, by tidal forces. The virtual particle becomes a real, measurable particle. If the energy for the virtual pair of particles comes from the black hole, the Hawking effect offers a possibility of extracting energy from the black hole. The lifespan of black holes is therefore limited! It is said that black holes can be caused by the emission of Hawking radiation**evaporate**(English term*black hole evaporation*).**(2)**The second interpretation establishes one**Black Hole Thermodynamics**, which has analogues to the main principles of classical thermodynamics. Hawking showed in 1973 that every black hole can be assigned a temperature proportional to its own**Surface gravity**is or inversely scaled with the mass of the black hole. The**Temperature of a black hole**is called the Hawking temperature, and it is therefore higher for small, light black holes. Every body of finite temperature is a**thermal radiator**(Heat radiator, Planck radiator). That's why this is**Hawking radiation spectrum**the same as that of a Planck radiator (thermal cavity radiation)!

So black holes evaporate by emitting Hawking radiation. However, the lifespan is already for black holes with solar mass (10^{30}kg) very high: it would be 10^{66}Years (around 10^{56}Hubble times!), Until such a black hole would be vaporized by Hawking radiation. The temperature of a stellar black hole is extremely low, namely only about a millionth of a Kelvin. Supermassive black holes in the core areas of galaxies have correspondingly even lower temperatures! A**direct detection**the Hawking radiation thus seems to be almost impossible.

But there could also be low-mass black holes, like the primordial black holes or**Mini holes**. Some cosmologists speculate that they formed in the early universe. Even smaller holes may soon be created in particle accelerators. All of these significantly lighter holes have a much shorter lifespan - down to the smallest fraction of a second. Mini-holes emit more than they absorb or collect through accretion. As a consequence, their mass gradually decreases. With a critical mass of 10^{14}g - which corresponds to a cosmically extremely small black hole - would be the black hole on ultra-short time scales of 10^{-23}Seconds to radiate its entire rest mass. This process is basically an explosion that 10^{35}erg releases. This energy scale is many decades below typical supernovae, hypernovae or gamma ray bursts; however, it should leave observable, certainly strongly red-shifted signatures on the distance scale of the early universe. Perhaps the infrared space telescope launched in 2003 will detect it*Sharpener*these traces of primordial black holes.

The energy of Hawking radiation depends on which particles materialize on the horizon. With the shrinking of the hole due to Hawking emission and the associated rise in temperature, the rest mass of various particle species is finally exceeded, so that a whole particle zoo is emitted.

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