We read in the last episode that black holes do not allow anything, not even light, to escape. Classically speaking, this is true. But when one applies the laws of quantum mechanics to black holes, one obtains a strange result — black holes are hot! They behave as though they have a non-zero temperature and emit radiation much like a heated piece of iron does. This result, first obtained by Stephen Hawking in the Seventies, is not completely understood yet and is a leading research area.

To understand this, we need to recall some results from thermodynamics, which govern the behaviour of, say, a gas at a finite temperature. A gas is made of a large number of molecules in random motion, which are colliding against each other and against the walls of the container, thus exerting a pressure. The temperature of the gas is essentially a measure of the average random speed of the molecules. To describe the physics of such a gas, one usually uses an average description in terms of the volume, pressure and temperature. This, of course, does not specify the microscopic state of the gas; for example, we almost never worry about the position and speed of each molecule. This lack of microscopic information can be quantified in terms of an entity called the “entropy” of the gas. The greater our lack of information about the microscopic state of the system, the higher is the entropy. The laws of thermodynamics then tell us how the entropy changes during the course of interactions. For example, if you let two gases mix, the entropy increases.

In the early Seventies, Jacob D. Bekenstein suggested that black holes also possess an entropy that is proportional to their surface area. This idea is closely linked to the fact that when a black hole is formed, it swallows up a lot of information about the initial state of the system. It was also known that when two black holes merge, say, the sum of their surface areas increases, just like the entropy increases when two gases are mixed. Bekenstein presented several arguments to back this idea and it looked very attractive.

There was, however, one problem. Usually, a system with a certain entropy and energy will also have a non-zero temperature and so we expect the black hole to have a temperature. But any object kept at a non-zero temperature will radiate energy with a characteristic pattern — called the thermal spectrum. (This is why an iron rod glows when it is heated.) But since the black hole is not supposed to emit any radiation, one should conclude that its temperature is zero! For this reason, people originally did not take Bekenstein’s idea seriously.

The situation, however, changes when you bring in quantum mechanics, which is what Hawking stumbled on. He found that a black hole does indeed emit radiation with precisely the thermal spectrum at a temperature that can be related to its mass. What is more, the temperature Hawking obtained, along with the entropy suggested by Bekenstein, fitted consistently with the laws of thermodynamics. The quantum black hole became a thermodynamical system, very much like a box of gas.

This has been one of the most intriguing results in theoretical high energy physics for nearly three decades now. One of the key (unresolved) questions is the following: In the case of a box of gas, one knows that there are a large number of molecules inside and — since we do not specify, for example, their positions — we are not giving complete information about the system when we use thermodynamics to describe the gas. It is this lack of information that manifests itself as the entropy of the gas. We do know, however, precisely what kind of internal structure exists in a gas and what kind of information is ignored. The corresponding problem in the case of the black hole is not yet solved — we do not know the internal degrees of freedom that contribute to the entropy of the black hole. You cannot solve this problem classically because it turns out that classically, the temperature of the black hole is zero and its entropy infinite. So, this is probably the first concrete problem in the interface of quantum theory and gravity. Many models for quantum gravity, including string theory, have attempted to attack this problem with varying levels of success but it is probably fair to say that we have a long way to go!

A closely related, but more difficult, question is: What will happen to a black hole? Classically, a collapsing star, which forms a black hole, will be crushed to infinite densities in a finite interval of time, as measured by an observer who was sitting on the surface of the star. The same process, however, takes infinite time as measured by an observer who is positioned far away. In fact, the latter observer will even claim that the black hole takes an infinitely long time to form! The situation is even more bizarre when we take into account the quantum effect, which attributes a finite temperature to the black hole. Now, since the black hole is radiating away its energy, which has to come from its mass, it should “evaporate” in finite time. But since different observers view these processes differently, it is not very clear how to interpret the black hole evaporation. These issues are still very much in debate among the researchers.

T. Padmanabhan is an astrophysicist at the Inter-University Centre for Astronomy and Astrophysics, Pune