NEWSPAPER obituaries of Subrahmanyan Chandrasekhar, who died last month aged 84, all highlighted the single achievement for which he will be best remembered 鈥� his work on white dwarf stars. He showed that these stars couldn鈥檛 exist if they weighed more than 1.4 times as much as the Sun. This immediately raised the question of what happened to much heavier stars when they ran out of fuel 鈥� did they go on contracting for ever until they became what we would now call a black hole?
Chandra, as he was always known, had his big idea when he was only 19, on the long sea voyage from India to England, where he took up a research studentship at the University of Cambridge. His early researches were indeed remarkable, and it was many years before they were fully appreciated. But they were just the beginning of a career spanning more than 60 years. Chandra earned a unique degree of respect among astrophysicists for his lifetime鈥檚 achievement, austere dedication and the consistently high standards he set. Indeed, it was the work he did when already in his sixties that Chandra himself rated most highly.
After his pioneering student work, Chandra shifted to other topics. His style of research was unusual. He would choose a subject, explore it thoroughly, and write up to fifty papers about it. He would then systematise his thoughts into a book and move on to something else. He produced classic texts on stellar structure, radiative transfer, the dynamics of stellar systems and other specialised topics.
Advertisement
Chandra鈥檚 intellectual stamina, combined with his self-disciplined neatness, allowed him to carry through the most elaborate mathematical manipulations without flagging and (equally remarkably) without mistakes. I recall the first time I heard him lecture, at a seminar in Cambridge. He presented his mathematics on slides, which he ran through at bewildering speed because each equation was too long to fit on a single slide, and spilled over onto several. He ended his talk with a typical disclaimer: 鈥淵ou may think I have used a hammer to crack eggs, but I have cracked eggs.鈥�
In a lecture on 鈥渃reativity鈥� on another occasion, Chandra quoted the great physicist Lord Rayleigh鈥檚 response to Thomas Huxley鈥檚 claim that 鈥渟cientists over 60 do more harm than good鈥�. Rayleigh (aged 67 at the time) had responded: 鈥淭hat may be, if he undertakes to criticise the work of younger men, but I do not see why it need be so if he sticks to the things he is conversant with.鈥� Chandra himself manifestly followed this precept.
The early 1970s were the 鈥渉eroic age鈥� of relativity research 鈥� theorists had proved that if Einstein was right, black holes weren鈥檛 infinitely diverse but standardised objects, characterised just as surely as any elementary particle by mass and spin. Astronomers already suspected that black holes were not just theoretical constructs, but actually existed in our Universe.
This made a deep impression on Chandra, aesthetically as well as scientifically. In a lecture in 1975 he said 鈥渋n my entire scientific life 鈥� the most shattering experience has been the realisation that an exact solution of Einstein鈥檚 equations of general relativity, discovered by the New Zealand mathematician Roy Kerr, provides the absolutely exact representation of untold numbers of massive black holes that populate the Universe. This 鈥榮huddering before the beautiful鈥�, this incredible fact that a discovery motivated by a search after the beautiful in mathematics should find its exact replica in Nature, persuades me to say that beauty is that to which the human mind responds at its deepest and most profound鈥� (Truth and Beauty, Chicago University Press, 1987).
Chandra was already in his sixties when he embarked on research on black holes. He never fully absorbed the mathematical techniques introduced by Roger Penrose at the University of Oxford, which had given the subject such impetus. Instead, he made his distinctive contribution by adapting the more 鈥渃lassical鈥� methods he had used in other contexts. He analysed how black holes respond when their equilibrium is perturbed, extending techniques that had traditionally been used to study the vibrations modes of a drum, or of the Earth and the oceans.
The techniques are, in a sense, complementary to the 鈥済lobal鈥� methods which Penrose pioneered: they cannot handle 鈥済eneric鈥� collapse, where there is no special degree of symmetry, but they do produce a more quantitative picture of what would happen if a black hole were perturbed (for instance, by, a smaller object falling into it or orbiting close to it). These techniques offer a 鈥減robe鈥� for black holes, just as seismologists can learn about the Earth鈥檚 structure from the various modes of oscillation when its crust is set 鈥渞inging鈥� after an earthquake.
Chandra鈥檚 mathematical virtuosity is dauntingly manifest in his 650-page treatise on The Mathematical Theory of Black Holes. In one chapter, 100 pages long, the manipulations are so heavy and the argument so terse that he adds the following footnote: 鈥淭he reductions that are necessary to go from one step to another [in this chapter] are often very elaborate and, on occasion, may require as many as ten, twenty, or even fifty pages. In the event that some reader may wish to undertake a careful scrutiny of the entire development, the author鈥檚 derivations (in some 600 legal-sized pages and in six additional notebooks) have been deposited in the Library of the University of Chicago.鈥�
Such is the interest surrounding Chandra and his subject that this formidable and recondite text has notched up thousands of paperback sales. Its sales are not, of course, in the class of Stephen Hawking鈥檚 Brief History of Time, but it has probably surpassed Hawking鈥檚 book in the ratio of copies sold to copies actually read. Any reader who perseveres would share the philosopher Alfred Whitehead鈥檚 reaction to the mathematics of Newton鈥檚 Principia: 鈥淚t was as though one was in an armoury where the weapons are of enormous size, and marvelling at one who wields as a weapon what we could barely lift as a burden.鈥�
Chandra was already 73 years old when his book on black holes appeared. Most of us suspected that this would be his final monograph 鈥� indeed, it rounded off his career with a fitting symmetry by codifying our understanding of the objects foreshadowed in what he had done fifty years earlier, when he was a student in Cambridge. But he continued, unflaggingly, his output of highly technical papers on relativity, especially on the theory of gravitational waves. He developed a new enthusiasm. His lifelong fascination with individuals who scale the supreme peaks of creativity, whether in science or the arts, led him to a detailed study of Newton鈥檚 works, which culminated in a 600-page exposition, published this summer, of Newton鈥檚 Principia.
Chandra intended his book on Principia to be his final one. Indeed, he had decided, at the age of 84, to bring his entire scientific efforts to a close. He was always critical of elderly scientists who 鈥渓ived on their reputation鈥�; a clean break was better than the risk of compromising his standards. His paper in the August issue of The Proceedings of the Royal Society was, he told colleagues, to be his last: 鈥淭here is a time for all things, and a time to end all things.鈥�
Perhaps he had planned to devote his remaining years to intensive reading of the great literature for which his arduous regime had never allowed time. Sadly, he has been denied this. But, as his obituarists have rightly noted, he will be remembered for his ideals and his example, as well as for his uniquely sustained and prolific contributions to astrophysics.