Episode 6: Hawking radiation

Today’s episode is about some of the more theoretical aspects of black holes, as compared to the astrophysical focus of Ep.5. The point of this week’s Episode 6 is to introduce for interested viewers the concept of Hawking radiation, invented by the famous dis/Abled British physicist Stephen Hawking.

General Relativity is a nonlinear theory, one in which the response of a system is not  proportional to the stimulus applied. (Climate is another good example of a highly nonlinear system.) This nonlinearity is important to GR’s ability to have black hole spacetimes in it, as physically allowed solutions of the Einstein Equations. After mentioning this tidbit, we describe an important property of black holes – the fact that they have no “hair”. There’s just the black hole, no frills or bling added. Observers outside of the event horizon can discern at most a measly three properties of the black hole: mass M, angular momentum J and (in the case of theory black holes rather than astrophysical ones) electromagnetic charge Q. No other information about what lies behind the horizon can leak out.

… Or can it?

Stephen Hawking’s famous insight was that quantum mechanics – the physics of the microscopic world – can indeed permit radiation of particles (massless or massive) from black hole horizons. Although, for astrophysical black holes the ensuing temperature of the radiation is extremely cold: significantly colder than the temperature of about 3 Kelvin of the Cosmic Microwave Background! The discovery of Hawking radiation totally rocked the world of researchers working on black holes, leading to breakthroughs in understanding the thermal physics of black holes and matter interacting with them. Interestingly, the temperature of smaller black holes is more fierce, raising the interesting question of what happens at the endpoint of runaway evaporation of small black holes. More on that later in the course.

The essence of Hawking radiation is the phenomenon of virtual pair production, which occurs in Nature even in the so-called “vacuum” where there are no [real] particles. I refer to pair production as “pair popping”, because the virtual particle-antiparticle pair pops into existence only for an extremely short time allowed by the Heisenberg Uncertainty Principle before it pops back out of existence, disappearing into the vacuum. The message here is that energy conservation can be violated in quantum processes, BUT ONLY if you do it so fast that quantum uncertainty lets you get away with the crime because no-one notices you’ve committed it.

Pair popping with both particle and antiparticle on the same side of the horizon is not the interesting phenomenon in the context of black holes. The interesting phenomenon is when a pair pops into existence straddling the horizon, and one pair is lucky enough to have sufficient momentum/energy to escape while its partner falls into the centre of the black hole. We show how, using the principle of energy conservation over macroscopic timescales, the black hole loses a little bit of its mass in a Hawking process.This is called Hawking evaporation.

The discovery of the Hawking temperature motivated theoretical physicists to study, armed with Gedankenexperiments, the thermodynamics of black holes. We introduce the thermodynamic concept of entropy, a measure of disorganization of a system (or, equivalently,  wasted heat in a thermal process). We explain in a bit of detail why it is physically useful to know about entropy in thermal systems. We explain that black holes, by virtue of their incredibly strong gravity in their densest parts, have a humongous entropy that is proportional to the area of their event horizon in units of the Planck scale, the tiniest imaginable distance at about 10^-35m. This black hole entropy somehow encodes the different possible ways that the black hole of given M, J, Q could have been formed from gravitational collapse of matter with mass, spin and force charges.

We finish with a discussion of the Black Hole Information Problem – which is caused by the fact that even outgoing Hawking radiation from a black hole horizon only knows those three data: M, J, Q. Even the Hawking radiation, the only thing apparently emitted by black holes, cannot carry sufficient information to recover data from matter thrown into black holes. We explicitly explain why this behaviour is very unlike that of a lump of coal, which is governed by the sensible rules of quantum electromagnetism, known as “QED” (Quantum ElectroDynamics). The BH Information Problem, which is still an extremely active area of forefront theoretical research (taking up a good fraction of my research time, for instance), poses yet another deep difficulty for Einstein’s theory of General Relativity. GR, as we explain, is only a classical theory of gravity. For an understanding of a quantum theory of gravity, and a deeper understanding of black hole singularities and horizons, we have to dig deeper. This is part of the motivation for the invention of string theory.

Here is a PDF file of my slides for this episode 6, and this is the narrated slideshow.