Hawking radiation

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v \- t \- e

Hawking radiation is a theoretical model for the decay and eventual dissolution of black holes over time, named for Stephen Hawking. It's relatively well-known among people with at least a rudimentary grasp of physics, but virtually everyone is fed a lies-to-children version of the explanation, which Hawking advanced to make the theory more understandable to laypeople.

## Contents

* 1 Common but incorrect explanation
* 2 Still oversimplified but decent explanation
* 3 How long will this take?
* 4 Evaporation time
* 5 In a nutshell
* 6 See also
* 7 External links
* 8 References

## Common but incorrect explanation[edit]

Space - that's all space, the void between galaxies and equally the space within and between the atoms of your body - is not empty. There is a constant creation/extinction of virtual particles (particle here can include energy as well). These particles come in particle-antiparticle pairs, which subsequently annihilate each other to respect energy conservation. If such a fluctuation occurs at the event horizon of a black hole and one falls into the black hole while the other escapes, the second particle becomes "real" and gains positive mass/energy while the former remains virtual and must assume negative mass/energy to maintain conservation of energy. Absorbing negative mass/energy makes a black hole less massive, meaning the "real" particle essentially carries a small amount of energy away from the black hole. Over time, this effect will eventually carry away all of the black hole's energy as these particles, thus dissolving it into nothing.[1]

## Still oversimplified but decent explanation[edit]

According to quantum field theory, spacetime possesses quantum fields that constantly fluctuate with energy like the ripples on an ocean, meaning no space is entirely empty; particles are simply dense concentrations of energy in the field. One can think of this field as vibrating with different modes of energy the way a string strung between two blocks can vibrate with different frequencies and shapes.[2] Normally, the positive- and negative-energy modes almost entirely cancel each other out, and the slight fluctuations remaining in the vacuum's quantum wave activity are commonly called "virtual particles"; in this sense, real particles are concentrations of extreme positive or negative energy where the quantum vacuum doesn't cancel itself.

Pinching a vibrating string forces a point on it to remain stationary, thus restricting the number of vibrational modes available to it. Because a black hole's mass is so large that its gravity utterly breaks spacetime, its event horizon similarly "pinches" the quantum fields around it and deprives them of some fundamental vibrational modes, preventing the quantum fields from cancelling themselves into a quantum vacuum. As particles are simply spots where the quantum fields don't almost cancel themselves into a quantum vacuum, this effect means black holes aren't physical objects but anomalies in quantum fields that produce particles from an area around them. These particles carry energy away from the quantum anomaly, essentially stealing energy from the black hole over time until it dissolves completely and the quantum fields almost cancel each other again.

## How long will this take?[edit]

The smaller the black hole is, the faster it radiates. The temperature of the radiation emitted by this effect is, for small objects up to some hundred stellar masses, extremely low (< 1 x 10-9 Kelvin). More massive holes like those existing in the centers of galaxies will have even lower temperatures. Of course, that means a really low power output, thus naturally a very difficult time detecting said radiation. Tiny black holes will evaporate quickly. The less massive they are, the more energetic their radiation will be.

As such, black holes will not begin to radiate until the temperature of the surrounding space (read: the cosmic microwave background, without matter infalling into them) is lower than the hole's, which will take quite a long time.[3]

For those who either are curious or are really bored and want to play with a calculator, the radiation temperature of a black hole is:

T H = ℏ c 3 8 π G M k B {\displaystyle T_{\mathrm {H} }={\frac {\hbar c^{3}}{8\pi GMk_{\mathrm {B} }}}}

## Evaporation time[edit]

The time that it would take Hawking radiation to evaporate a black hole depends entirely on its mass:

t ev = 5120 π G 2 M 0 3 ℏ c 4 ≈ 2.1 × 10 67 years ( M M ⊙ ) 3 {\displaystyle t_{\operatorname {ev} }={\frac {5120\pi G^{2}M_{0}^{3}}{\hbar c^{4}}}\approx 2.1\times 10^{67}\,{\text{years}}\ \left({\frac {M}{M_{\odot }}}\right)^{3}}

Thus, a black hole with one Solar mass (2 x 1030 kg) would last for roughly 2 x 1067 years, while a black hole with a mass of 1 gram would last for 8 x 10-26 seconds.

## In a nutshell[edit]

## See also[edit]

* Astronomy
* Subatomic particle

## External links[edit]

* Wikipedia's article on Hawking radiation, which gives a much more detailed mathematical explanation.
* Hawking radiation calculator.

## References[edit]

1. ↑ Hawking radiation
2. ↑ What are modes of vibration? - McLaskey research group
3. ↑ A black hole would be immune to evaporation if its temperature were lower than the absolute lowest one that, as noted in the article about the future of the Universe, the latter would reach in the case of eternal accelerated expansion (10-29K). However, such a hypothetical black hole would need to have a mass of at least 1.22 x 1052kg (6.1 x 1022 solar masses, around 1/10 of the mass of ordinary matter in the Observable Universe), and its Schwarzschild radius would be roughly 1.9 billion light years, larger than the cosmological horizon of those times. Were such accelerated expansion to end, so the Universe's temperature could decrease indefinitely, even such monstrous black hole would evaporate away given enough time (by inputting numbers in the next equation, after around 4.8 x 10135 years). Nothing lasts forever.