Wednesday, April 7, 2021

What is the Hawking radiation?

Hawking radiation is black-body radiation that is predicted to be released by black holes, due to quantum effects near the black hole event horizon. It is named after the physicist Stephen Hawking, who provided a theoretical argument for its existence in 1974.
Hawking radiation is required by the Unruh effect and the equivalence principle applied to black hole horizons. Close to the event horizon of a black hole, a local observer must accelerate to keep from falling in.

An accelerating observer sees a thermal bath of particles that pop out of the local acceleration horizon, turn around, and free-fall back in. The condition of local thermal equilibrium implies that the consistent extension of this local thermal bath has a finite temperature at infinity, which implies that some of these particles emitted by the horizon are not reabsorbed and become outgoing Hawking radiation.


When particles escape, the black hole loses a small amount of its energy and therefore some of its mass. Consequently, an evaporating black hole will have a finite lifespan. By dimensional analysis, the life span of a black hole can be shown to scale as the cube of its initial mass, and Hawking estimated that any black hole formed in the early universe with a mass of less than approximately 1015 g would have evaporated completely by the present day.

The requirement that black holes lose energy into the wider universe, and therefore can “evaporate”, and the radiated spectrum are both a result of analysing black hole thermal equilibrium combined with extreme redshifting effects very close to the event horizon, with some consideration of quantum entanglement effects.

A pair of virtual waves/particles arises just outside the event horizon due to ordinary quantum effects. Very close to the event horizon, these always manifest as a pair of photons. It may happen that one of these photons passes beyond the event horizon, while the other escapes into the wider universe (“to infinity”).

A close analysis shows that the exponential red-shifting effect of extreme gravity very close to the event horizon almost tears the escaping photon apart, and in addition very slightly amplifies it. The amplification gives rise to a “partner wave”, which carries negative energy and passes through the event horizon, where it remains trapped, reducing the total energy of the black hole. The escaping photon adds an equal amount of positive energy to the wider universe outside the black hole.

In this way, no matter or energy ever actually leaves the black hole itself. A conservation law exists for the partner wave, which in theory shows that the emissions comprise an exact black body spectrum, bearing no information about the interior conditions.

Hawking radiation reduces the mass and rotational energy of black holes and is therefore also known as black hole evaporation. Because of this, black holes that do not gain mass through other means are expected to shrink and ultimately vanish. For all except the smallest black holes, this would happen extremely slowly.

The radiation temperature is inversely proportional to the black hole’s mass, so micro black holes are predicted to be larger emitters of radiation than more massive black holes and should thus shrink and dissipate faster.

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