Relativity and the Quantum / Elementary Tour part 2: Evaporating black holes?

Can the concepts of relativistic quantum field theory be carried over to curved spacetimes, which include gravitational sources and are described by general relativity? The answer is a cautious “yes”. The most notable step in this direction was taken by the British physicist Stephen Hawking in the 1970s.

Hawking examined a model of quantum particles not in the gravity-free environment of special relativity, but in a spacetime containing a black hole. The result was surprising: The mere presence of the black hole means that, even if at early times not a single particle was present, at late times, there is a steady stream of them escaping to infinity. In other words: a black hole emits quantum particles! This conjectured radiation is known as “Hawking radiation”. While it has not yet been observed, convincing reasons for its existence appear to be built right into the foundations of quantum theory.

The greater the mass of the black hole, the lower the temperature and intensity of Hawking radiation. The following table shows a few black hole masses, corresponding Schwarzschild radii (which measure the size of a spherical black hole) and the temperature (measured in Kelvin) of the radiation it emits. Each entry has as a background the characteristic color of thermal radiation with the given temperature:

mass Schwarzschild radius temperature
solar mass 3 kilometres (1.9 miles) 1 tenth of a millionth Kelvin
mass of the earth 9 millimetres 0.02 Kelvin
mass of the moon 1/10 millimetres 1.7 Kelvin
1/10 mass of the moon 1/100 millimetre 17 Kelvin
1/100 mass of the moon 1 millionth of a metre 170 Kelvin
1/1000 mass of the moon 1/10 millionth of a metre 1700 Kelvin
1/2000 mass of the moon 1/20 millionth of a metre 3300 Kelvin
1/5000 mass of the moon 1/50 millionth of a metre 8400 Kelvin

As the colours show, astrophysical black holes – such as stellar and supermassive black holes – are indeed black. Black holes lighter than about a hundredth of the mass of the earth’s moon, however, glow in the dark. Even lighter ones – a five-thousandth the mass of the moon – are white-hot objects, and look the part. For holes that are lighter still, most radiation is emitted as UV radiation, X-rays or even highly energetic gamma radiation.

The table doesn’t indicate intensities. In fact, the black holes shown are rather dark. For black holes with lesser masses, however, significant fractions of mass and energy are radiated away – the smaller the mass, the greater the power. This leads to a runaway process with a final, gigantic flash of energy in which the black hole evaporates.

If, in our universe’s fiery youth, “mini black holes” of very little mass had formed, some might now have reached the stage where such violent evaporation occurs. So far, though, no astronomical evidence for highly energetic evaporation processes has been found, and Hawking radiation remains purely theoretical.

In calculations like Hawking’s initial derivation of radiating black holes, matter is described in quantum terms, but the concepts of classical general relativity are used to describe the spacetime environment. However, there are situations when this semi-classical treatment is insufficient. To fully understand our universe, these situations indicate that it is necessary to formulate a quantum theory of gravity, in which space and time are subject to the laws of the quantum world as well.