The image of Stephen Hawking – who has died aged 76 – in his motorised wheelchair, with head contorted slightly to one side and hands crossed over to work the controls, caught the public imagination, as a true symbol of the triumph of mind over matter. As with the Delphic oracle of ancient Greece, physical impairment seemed compensated by almost supernatural gifts, which allowed his mind to roam the universe freely, upon occasion enigmatically revealing some of its secrets hidden from ordinary mortal view.
Of course, such a romanticised image can represent but a partial truth. Those who knew Hawking would clearly appreciate the dominating presence of a real human being, with an enormous zest for life, great humour, and tremendous determination, yet with normal human weaknesses, as well as his more obvious strengths. It seems clear that he took great delight in his commonly perceived role as “the No 1 celebrity scientist”; huge audiences would attend his public lectures, perhaps not always just for scientific edification.
The scientific community might well form a more sober assessment. He was extremely highly regarded, in view of his many greatly impressive, sometimes revolutionary, contributions to the understanding of the physics and the geometry of the universe.
Hawking had been diagnosed shortly after his 21st birthday as suffering from an unspecified incurable disease, which was then identified as the fatal degenerative motor neurone disease amyotrophic lateral sclerosis, or ALS. Soon afterwards, rather than succumbing to depression, as others might have done, he began to set his sights on some of the most fundamental questions concerning the physical nature of the universe. In due course, he would achieve extraordinary successes against the severest physical disabilities. Defying established medical opinion, he managed to live another 55 years.
His background was academic, though not directly in mathematics or physics. His father, Frank, was an expert in tropical diseases and his mother, Isobel (nee Walker), was a free-thinking radical who had a great influence on him. He was born in Oxford and moved to St Albans, Hertfordshire, at eight. Educated at St Albans school, he won a scholarship to study physics at University College, Oxford. He was recognised as unusually capable by his tutors, but did not take his work altogether seriously. Although he obtained a first-class degree in 1962, it was not a particularly outstanding one.
He decided to continue his career in physics at Trinity Hall, Cambridge, proposing to study under the distinguished cosmologist Fred Hoyle. He was disappointed to find that Hoyle was unable to take him, the person available in that area being Dennis Sciama, unknown to Hawking at the time. In fact, this proved fortuitous, for Sciama was becoming an outstandingly stimulating figure in British cosmology, and would supervise several students who were to make impressive names for themselves in later years (including the future astronomer royal Lord Rees of Ludlow).
Sciama seemed to know everything that was going on in physics at the time, especially in cosmology, and he conveyed an infectious excitement to all who encountered him. He was also very effective in bringing together people who might have things of significance to communicate with one another.
When Hawking was in his second year of research at Cambridge, I (at Birkbeck College in London) had established a certain mathematical theorem of relevance. This showed, on the basis of a few plausible assumptions (by the use of global/topological techniques largely unfamiliar to physicists at the time) that a collapsing over-massive star would result in a singularity in space-time – a place where it would be expected that densities and space-time curvatures would become infinite – giving us the picture of what we now refer to as a “black hole”. Such a space-time singularity would lie deep within a “horizon”, through which no signal or material body can escape. (This picture had been put forward by J Robert Oppenheimer and Hartland Snyder in 1939, but only in the special circumstance where exact spherical symmetry was assumed. The purpose of this new theorem was to obviate such unrealistic symmetry assumptions.) At this central singularity, Einstein’s classical theory of general relativity would have reached its limits.
Meanwhile, Hawking had also been thinking about this kind of problem with George Ellis, who was working on a PhD at St John’s College, Cambridge. The two men had been working on a more limited type of “singularity theorem” that required an unreasonably restrictive assumption. Sciama made a point of bringing Hawking and me together, and it did not take Hawking long to find a way to use my theorem in an unexpected way, so that it could be applied (in a time-reversed form) in a cosmological setting, to show that the space-time singularity referred to as the “big bang” was also a feature not just of the standard highly symmetrical cosmological models, but also of any qualitatively similar but asymmetrical model.
Some of the assumptions in my original theorem seem less natural in the cosmological setting than they do for collapse to a black hole. In order to generalise the mathematical result so as to remove such assumptions, Hawking embarked on a study of new mathematical techniques that appeared relevant to the problem.
A powerful body of mathematical work known as Morse theory had been part of the machinery of mathematicians active in the global (topological) study of Riemannian spaces. However, the spaces that are used in Einstein’s theory are really pseudo-Riemannian and the relevant Morse theory differs in subtle but important ways. Hawking developed the necessary theory for himself (aided, in certain respects, by Charles Misner, Robert Geroch and Brandon Carter) and was able to use it to produce new theorems of a more powerful nature, in which the assumptions of my theorem could be considerably weakened, showing that a big-bang-type singularity was a necessary implication of Einstein’s general relativity in broad circumstances.
A few years later (in a paper published by the Royal Society in 1970, by which time Hawking had become a fellow “for distinction in science” of Gonville and Caius College, Cambridge), he and I joined forces to publish an even more powerful theorem which subsumed almost all the work in this area that had gone before.
In 1967, Werner Israel published a remarkable paper that had the implication that non-rotating black holes, when they had finally settled down to become stationary, would necessarily become completely spherically symmetrical. Subsequent results by Carter, David Robinson and others generalised this to include rotating black holes, the implication being that the final space-time geometry must necessarily accord with an explicit family of solutions of Einstein’s equations found by Roy Kerr in 1963. A key ingredient to the full argument was that if there is any rotation present, then there must be complete axial symmetry. This ingredient was basically supplied by Hawking in 1972.
The very remarkable conclusion of all this is that the black holes that we expect to find in nature have to conform to this Kerr geometry. As the great theoretical astrophysicist Subramanyan Chandrasekhar subsequently commented, black holes are the most perfect macroscopic objects in the universe, being constructed just out of space and time; moreover, they are the simplest as well, since they can be exactly described by an explicitly known geometry (that of Kerr).
• Stephen William Hawking, physicist, born 8 January 1942; died 14 March 2018, aged 76.