Today, the world lost a physicist of the highest calibre in Stephen Hawking. He was the inspiration for a generation of physicists, ranging from undergraduate students dreaming of fascinating concepts such as the big bang and black holes to professional physicists who are constantly grappling with such ideas. Hawking made significant contributions to theoretical physics, specifically, in the areas that lie at the interface of gravitation and quantum theory.
In the popular narrative, Hawking may be well remembered for his best-selling book A Brief History of Time and, say, for his occasional appearances on The Big Bang Theory. I believe that the best way of paying tribute to a person is to highlight an idea that they created. Which is why in this brief piece, I describe a concept that is arguably the primary contribution of Hawking to theoretical physics, viz. that black holes emit thermal radiation, which, in his honor, is referred to as Hawking radiation.
Hawking was a doctoral student of Dennis Sciama at Cambridge in the mid-1960's. As a part of his doctoral thesis, Hawking had investigated the nature of so-called singularities that arise in the relativistic theory of gravitation formulated by Einstein — otherwise known as general relativity. In general relativity, gravity is characterized as the geometry of spacetime. According to the theory, the presence of matter curves spacetime and the strength of gravity is reflected by the extent to which the spacetime is curved. The singularities are domains where matter has collapsed to a very high density resulting in a curvature so large that the concept of spacetime loses its meaning near them.
If the spacetime can be imagined to be a curved sheet of paper, the singularities would correspond to locations with sharp edges (or even tears) that arise when the paper is crumpled. As it gets difficult to describe the geometry of the paper near the sharp edges, it becomes difficult to understand the nature of spacetime near singularities. Such singularities are expected to occur in black holes which are supposed to have been formed say, when stars with a large initial mass collapse to form compact objects. Why is this important? Because according to modern cosmology — encapsulated in the big bang model -- our universe is supposed to have originated from a singularity. In the late 1960's, Hawking, along with Roger Penrose, established the so-called area theorems, which, for instance, suggest that the areas of black holes always increase.
In the early 1970's Hawking, along with co-workers, noticed that the laws governing the dynamics of black holes were akin to the laws of thermodynamics which describe systems that do work and exchange heat. The formulation of these laws motivated Jacob Bekenstein, then a graduate student working under the supervision of John Wheeler at Princeton, to closely examine the nature of black holes from the thermodynamic viewpoint. According to the famous second law of thermodynamics, the entropy of a system — i.e. the extent of its disorder — remains the same or increases when it is left alone. (We encounter this phenomenon even in our daily lives — unless we do work our rooms have a tendency to get disorganized!) In classical physics, black holes are perfectly black — they absorb anything, but emit nothing.
If so, Bekenstein argued that one can violate the second law of thermodynamics simply by dropping a hot cup of coffee (which carries heat and, therefore, entropy) into a black hole. In order to circumvent this difficulty, Bekenstein proposed that, not only do black holes carry entropy (proportional to their area), it is the sum of the entropy of the black holes and the entropy of matter outside that remains the same or increases, a concept that has since come to be known as the generalized second law of thermodynamics.
In thermodynamics, objects which carry entropy also possess heat. This implies that objects with entropy may also radiate heat. In contrast, black holes, though they possess entropy, do not seem to emit anything, i.e. carry no temperature, which is a strange situation from a thermodynamic viewpoint. It is in such a situation that Hawking's genius came to the fore in the mid 1970's. Until then black holes were solely considered from a classical perspective. Hawking discovered that, when one studies
behavior of fields (such as, say, the electromagnetic fields describing light) from a quantum perspective, not only do black holes cease to remain black, they emit radiation with a thermal characteristic exactly as expected from the otherwise classical laws of black hole thermodynamics.
As Hawking has himself explained in his popular book A Brief History of Time, this phenomenon is not very difficult to understand. Black holes are surrounded by a one-way membrane called the event horizon, which ensures that, while objects can go in, even light cannot emerge. In contrast to classical mechanics, quantum mechanics involves a certain level of indeterminacy, which manifests itself as fluctuations. For instance, virtual pairs of particles (such as an electron-positron pair) can emerge out of nothing, annihilating themselves soon after. However, near the event horizon of a black hole, one finds that pairs of virtual particles are converted into real pairs, with one of them falling into the black hole and the other traveling to infinity leading to Hawking radiation.
Since its original discovery, various investigations have suggested that the thermal nature of black holes can be attributed to the event horizon and, in fact, Hawking radiation is also encountered in other spacetimes with such horizons. Soon after his work on thermal radiation from black holes, Hawking had also suggested that the radiation can lead to loss of information, as matter is converted to heat. After all, a burning paper can be described only by its temperature, destroying the information that it could have carried originally. This proposal has come to be known as the information loss paradox and it remains an issue yet to be resolved, despite more than forty years of scrutiny.
In this brief article aimed at a general reader, I have outlined the theoretical idea of thermal emission from black holes, which can be considered to be the most profound contribution of Stephen Hawking.
(L Sriramkumar is a Professor of Physics at the Indian Institute of Technology Madras, Chennai. He was a doctoral student of T Padmanabhan, and works on various aspects of Gravitation and Cosmology. He has been a post-doctoral fellow of Jacob Bekenstein (who proposed the concept of black hole entropy, referred to as the Bekenstein-Hawking entropy) and Don Page (a doctoral student of Stephen Hawking, who has, for instance, examined the thermal properties of certain spacetimes leading to a concept called the Hawking-Page phase transition)
