Question 41.11: Hawking Radiation Is NOT Science Fiction In the previous exa......

Hawking Radiation Is NOT Science Fiction

In the previous example, we imagined a whole meal being created from nothing. The result was that such a meal could only exist for a negligible amount of time.

But don’t think that such events are impossible. The British physicist Stephen Hawking has a theory that predicts radiation from black holes. Recall from Section 39-12 that nothing can escape from the event horizon of a black hole. However, Hawking theorizes that black holes can radiate; we call this radiation Hawking radiation. His idea is that particle and antiparticle pair are created out of nothing near the event horizon of a black hole. Normally, when a particle and antiparticle are created, they soon come together and annihilate one another. But if in their short lifetime one of the particles falls inside the event horizon, the other particle will escape.

In principle we could see this escaped particle as Hawking radiation from the black hole. This radiation carries energy away from the black hole. Thus the black hole effectively loses energy and its mass is reduced, and we say the black hole evaporates. This evaporation process is very slow for solar mass black holes; such a black hole would take over 10^{67} years to evaporate. The universe is only 13.7 billion years old, and so no solar mass black holes have evaporated. However, much lower mass black holes known as primordial black holes may have had enough time to evaporate. Such small black holes would produce a final burst of high-energy Hawking radiation. Although no such radiation has been observed yet, it is theoretically possible.

Consider the creation of an electron-position pair near a black hole. Similar to the writer’s idea about the meal in Example 41.10, one of the particles must be consumed by the black hole in their brief lifetime. Estimate the lifetime of such an electron-positron pair.