A brief history of Stephen Hawking's work

A brief history of Stephen Hawking's work

The death of Stephen Hawking leaves a void that would be difficult to fill. He died on March 14, at the age of 76, coincidentally the day Einstein was born. Hawking was born in January 1942, and as he pointed, exactly 300 years after the death of Galileo in 1642. Although these dates are coincidental, there is little doubt that posterity would rank Hawking in a similar category as Galileo, Einstein or Newton. However, in contrast to these all-time greats, Hawking's accomplishments are in spite of the physical challenges he faced due to Lou Gehrig's disease, a rare neurological disease.

He collaborated with the well known British physicist, Roger Penrose, on the Hawking-Penrose singularity theorems. This showed that gravitational collapse of a sufficiently massive star cannot be halted and would inevitably collapse to a singular state of infinite density. All geodesics would be incomplete and converge to this singular state. They arrived at this result from general assumptions about the physical properties of the collapsing matter.  

Just as the future of the gravitational collapse is a singularity in the future, the universe began with a singularity in the past. The same theorems imply that the currently expanding universe had a singularity in the past when quantities like density and curvature assumed infinitely large values. Hawking and Penrose showed that, very generally, in the strict framework of Einstein's general theory of relativity, future and past singularities were inevitable.

In the case of black holes, the singularity is shielded by the presence of an event horizon, which is a well-defined surface of a black hole, within which nothing can be seen and nothing can escape. All information about what type of matter went inside the event horizon is lost to the outside world. Whether you fill the black hole with elephants, buildings or anything else, the only information you can get is the total mass that went inside.

An early discovery made by Hawking is the area theorem that underlies black holes. He showed that when two black holes merge or interact, they would do so in such a way that the total surface area of their event horizons (their surfaces) can never decrease. It can only lead to the formation of larger black holes. It also constrains the maximum energy that can be released through the interaction of two black holes. Most importantly, the work showed that black holes cannot be ripped apart but can only become bigger.

Hawking also had the idea that this area theorem where total areas of black hole surfaces cannot decrease is strikingly analogous to the second law of thermodynamics, wherein the total entropy of a thermodynamic system cannot decrease.

The problem arose that if you associate black hole area with entropy, what is the analogue of temperature? You cannot talk of entropy without a corresponding temperature. While trying to unravel this puzzle, Hawking made a surprising discovery. He showed that black holes don't radiate only if you consider the classical picture.

If quantum theory is included, a black hole could indeed radiate. This is in a sense analogous to quantum tunnelling which is pervasive in nuclear and condensed matter phenomena.  For instance, it was difficult to understand why heavy nuclei undergo radioactive decay. The alpha particles emerging out have far less energy than required to overcome the potential barrier of the strong nuclear forces binding nuclei. Though classically forbidden, in quantum theory, a particle can tunnel out of the barrier. Moreover, the strong gravitational field outside a black hole can create particle pairs, one of which falls into the hole while the other escapes. In short, Hawking showed that a black hole radiates like a black body with a temperature inversely proportional to its mass.

For solar mass black hole, this temperature is hardly a millionth of a degree. But another idea he had is that in the early universe, when temperatures and densities were extreme, primordial black holes with all masses could have formed. An asteroid mass black hole would have a temperature of a trillion degrees and could now be generating a burst of gamma rays. However, despite many searches, this theory has not been observed yet.

Hawking's other work deals with cosmological aspects like a wave function for the universe and on inflation models. His attempts to quantify gravity and space time are seminal with implications for the universe.

(The author is with Indian Institute of Astrophysics, Bengaluru)

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