The Hawking radiation process

We now outline the steps in the Hawking radiation process, which leads to the automatic creation of remnants

Outline of the physics involved in the Hawking process :   

(a) If we place a particle \( m \) sufficiently close to a heavy mass \( M \) then the net energy of \( m \) is negative. By placing many such particles \( m \), we can reduce the total energy of the system to zero, or close to zero. Such small energy objects are called 'remnants' and are generally a problem for physics.

(b) If we use only classical physics, then it is not clear how to place \( m \) at the desired position. In particular, we cannot get the desired configuration if \( m \) is 'dropped in' or 'lowered in by a rope'.

(c) Hawking noted that quantum fluctuations near the horizon create particle pairs. This pair does not have to annihilate; it can last for ever since the net energy of the pair is \( \Delta E=0 \).

(d) One member of the created pair escapes away from the hole. Such particles emanating from the horizon are called 'Hawking radiation'.

(e) The other member of the pair gets automatically placed inside the hole in the manner required to make a remnant. In classical physics we had to bring in the particle from outside, and we saw that this did not allow a net negative energy for \( m \). But in the Hawking process, the particle is generated from the vacuum by a quantum fluctuation near the horizon. So it is automatically placed at the correct position where it can have a negative net energy.

(f) The net energy of the hole decreases each time we place another negative energy particle inside the horizon. The particle that escaped the hole had a positive energy, so energy is conserved overall. We may say that the hole radiates away its energy by the process of Hawking radiation.

(g) At the end of the radiation process, we are left with a 'remnant' which has a small mass or a zero mass.

The following gives a summary of the Hawking process in pictures