General relativity is arguably the most beautiful scientific theory ever conceived but its status within mainstream physics has vacillated since it was proposed in 1915. It began auspiciously with the successful explanation of the precession of Mercury and the dramatic confirmation of light-bending in the 1919 solar eclipse expedition, which turned Einstein into an overnight celebrity. Though little noticed at the time, there was also Karl Schwarzschild's discovery of the spherically symmetric solution in 1916 (later used to predict the existence of black holes) and Alexander Friedmann's discovery of the cosmological solution in 1922 (later confirmed by the discovery of the cosmic expansion).Then for 40 years the theory was more or less forgotten, partly because most physicists were turning their attention to the even more radical developments of quantum theory but also because the equations were too complicated to solve except in situations involving special symmetries or very weak gravitational fields (where general relativity is very similar to Newtonian theory). Furthermore, it was not clear that strong gravitational fields would ever arise in the real universe and, even if they did, it seemed unlikely that Einstein's equations could then be solved. So research in relativity became a quiet backwater as mainstream physics swept forward in other directions. Even Einstein lost interest, turning his attention to the search for a unified field theory.This book tells the remarkable story of how the tide changed in 1963, when the 28-year-old New Zealand mathematician Roy Kerr discovered an exact solution of Einstein's equations which represents a rotating black hole, thereby cracking the code of the title. The paper was just a few pages long, it being left for others to fill in the extensive beautiful mathematics which underlay the result, but it ushered in a golden age of relativity and is now one of the most cited works in physics. Coincidentally, Kerr's breakthrough was not the only one in 1963 because Maarten Schmidt also discovered the first quasar, 3C273. By recognizing its redshifted spectrum and hence its huge cosmological distance, he demonstrated that some stupendous source of energy was required. Nowadays, most astrophysicists assume this must involve a supermassive black hole of the kind Kerr discovered, so it was a serendipitous combination of theoretical and observational developments that placed general relativity once more at centre-stage.Both discoveries were announced at the First Texas Symposium of Relativistic Astrophysics in Dallas in December 1963 but met with very different receptions. Schmidt's report generated huge excitement and was the main focus of the meeting. By contrast, Kerr's report was a mere 10-minute presentation – its importance appreciated only by the small group of relativists present, including Achilles Papapetrou, who admonished the audience for giving the talk such a lukewarm reception. Indeed, Kerr nearly didn't speak at all since Roger Penrose had originally been asked to report on his new solution as part of an overview talk.Nevertheless, Kerr's discovery proved to be of equal importance in the burgeoning field of relativistic astrophysics and it soon spawned dozens of other important papers. Indeed, by the time John Wheeler coined the phrase `black hole' in 1967, many of the well-known properties of the Kerr solution – the rotating event horizon, the ring singularity, the inner horizon, the closed timelike curves and the ergosphere – had already been established. The solution was also generalized to the electrically charged case by Ted Newman. Most remarkably, work by Werner Israel, Brandon Carter and Stephen Hawking showed that the Kerr–Newman solution represents the unique end-state of rotating collapsing matter. This means that black holes (unlike other astronomical objects) can be completely described by their mass, angular momentum and charge. This so-called `no hair theorem' explains why Kerr's discovery is so important.Today 15000 quasars are known and all are thought to be powered by Kerr black holes. Indeed, a large fraction of the x-ray background detected by the Chandra satellite is thought to have been generated by such holes, in which case there could 300 million of them in the observable universe. Subrahmanyan Chandrasekhar, after whom the satellite is named, best expressed the situation [1]: `the most shattering experience has been the realization that an exact solution of Einstein's equations of general relativity…provides the absolutely exact representation of untold numbers of black holes that populate the universe'.The account so far will be very familiar to most relativists. However, probably very few know the full story of the events leading up to Kerr's great discovery and that is what this fascinating and informative book provides. It adds three important elements to the usual accounts: it describes the personalities involved, it explains how the solution was found, and it puts the episode in a broader historical context. I will now discuss these elements in turn.Focusing on the personalities is important because science is a very human endeavour – involving passion, excitement, missed opportunity, serendipidity and sometimes tragedy – and this story has all of these elements. The central character is Kerr himself, who provides his own afterword to the book. Surprisingly, he was not originally a relativist at all but a pure mathematician. After his undergraduate studies at the University of Canterbury in Christchurch, he started a PhD in group theory at Cambridge. However, it was during this period that he was introduced to relativity by his friend John Moffatt and then further enthused by an influential seminar on gravitational radiation by Felix Pirani at King's College London. A sequence of postdoctoral positions in the USA followed, culminating in his move to Alfred Schild's Center for Relativity in Austin, Texas, where he wrote his seminal paper.The second strength of this book is that it shows how Kerr's discovery related to other developments in the field. Progress in physics is rarely made in isolation and there is a strong supporting cast in this drama. The key to his breakthrough was the simplification of Einstein's equations entailed in studying what are termed `shear-free' solutions. The first clue came from Ray Sachs, whose studies of asymptotically shear-free bundles of light-rays reduced Einstein's equations to manageable form. Ivor Robinson and Andrzej Trautman then considered bundles which are shear-free everywhere but they were looking for solutions with gravity waves rather than time-independent ones and so missed the great discovery.Kerr learnt about these developments at a 1962 meeting on Gravitation and General Relativity in Warsaw, which clearly played a seminal role in the development of his ideas. But what most excited him was the enthusiastic summary of Vitaly Ginzburg, extolling the virtues of general relativity and emphasizing the need to understand strong gravity effects such as rotation. In any case, he returned to Austin convinced that he had the tools required to solve the problem. At first, he was discouraged when Newman claimed to prove that no shear-free space is possible but fortunately Kerr found a mistake in this work. By using coordinates which incorporated the rotational symmetry of the problem, he was able to find an exact solution in which the metric contains an event horizon and is asymptotically rotating.Since the Warsaw meeting played such a crucial role, it is interesting to recall that Richard Feynman also attended the meeting and described it in rather unflattering terms in a letter to his wife [2]: `I am not getting anything out of the meeting. I am learning nothing. Because there are no experiments, this field is not an active one, so few of the best men are doing work in it. The result is that there are hosts of dopes here and it is not good for my blood pressure…remind me not to come to any more gravity conferences!'. The book does not mention this but Feynman's negativity may have resulted from the fact that he attended the meeting primarily to present his early work on quantum gravity. This did not excite the relativists as much as he had hoped, so this may have generated some antipathy. Nevertheless, his impression is interesting because it reflects the prevailing opinion at the time that relativity had made little progress since the 1930s. Feynman clearly did't recognize the significance of the Pound–Rebka experiment (which had recently measured the slowing down of time in the gravitational field of the Earth) or appreciate that a new band of young relativists were instilling fresh energy into the field, unintimidated by the fear (prevalent at the time) of what Einstein might say about their endeavours.The third strength of this book is that it puts Kerr's discovery in broader historical context. It starts with a useful discussion of the earlier development of ideas in special and general relativity. Most of this is well known but it also includes some points which are rarely described in popular accounts. Of particular interest is Melia's account of the exchanges between Einstein and the mathematician David Hilbert in 1915. He suggests that Hilbert may have submitted a paper containing the correct equations of general relativity five days earlier than Einstein, although this is controversial since Einstein's paper was certainly published first and Hilbert may well have modified his own paper after reading it [3]. It is also good to stress the contribution of Emmy Noether, who first found the connection between symmetries and conservation laws. This is described in a book by Leon Lederman and Chris Hill [4] as `certainly one of the most important mathematical theorems ever proved in guiding the development of modern physics'. Since Kerr was himself a mathematician, one important message of this book (at least implicitly) seems to be the fundamental importance of mathematics in the development of physics. This is very topical in view of the current controversy over whether string theory should be regarded as mathematics or physics.One might question Melia's assertion that the golden age initiated by Kerr ended in the mid-1970s. Certainly the detection of stellar black holes, the discovery of the binary pulse PSR 1913+16, the precise measurement of the slowing down of time in a gravitational field by Gravity Probe A, and the discovery of black hole quantum radiation all came in this period. However, in some ways relativity is still enjoying a golden age: it is just that most research now focuses on numerical relativity, gravitational waves and quantum gravity rather than looking for exact solutions of Einstein's equations. For example, the detection of gravitational waves will surely herald another golden age within the next few years.What is true is that old-fashioned classical relativity has again moved to the side-lines and this raises an interesting point. In the search for a unified theory, either quantum theory or relativity must triumph because they are incompatible. Some people (in particular, the string theorists) feel that quantum theory will eventually triumph, with general relativity just representing a first level of approximation to the final picture. However, others (e.g., Roger Penrose and proponents of loop quantum gravity) feel that general relativity will turn out to be more fundamental. It is too soon to decide which side is correct. There are clearly further codes to break.Finally, what has become of the code-breaker himself? Kerr maintained links with Austin until 1977 when Schild died. By then he had become disillusioned with the aggressive nature of science in America. Nor was the aggression confined to the ivory towers of academia, since he was in Austin in 1966, when a crazed gunman in the university tower shot several people dead, one of whom was Kerr's fellow-relativist Robert Boyer. He returned to the University of Canterbury in 1971, where he headed the Mathematics Department until his retirement in 1993. He remains a colourful character, whose interests go well beyond relativity. Indeed, his first love is now rumoured to be bridge!To an end on a personal note, I've always felt a close affinity with Kerr because his surname is a variant of my own. This has sometimes had amusing consequences. On a trip to China in 1985, I was surprised when one of my talks attracted a huge audience. It later transpired that I had been confused with my more famous near name-sake!References[1] Chandrasekher S 1987 Truth and Beauty: Aesthetics and Motivations in Science (Chicago, IL: University of Chicago Press)[2] Feynman, RP 1988 What Do You Care What Other People Think? (New York, NY: Norton Press)[3] Corry L, Renn J and Stachel J, 1997 Belated decision in the Hilbert--Einstein priority dispute Science278 1270[4] Lederman L M and Hill C T 2004 Symmetry and the Beautiful Universe (New York, NY: Prometheus Books)