Black holes always make for an interesting read. This is true for both professional researchers and for members of the public, whose fascination with these curious objects has filled so many shelves in bookshops’ science sections. Yet before the appearance of Fulvio Melia’s Cracking the Einstein Code, little had been written about the man who did so much to explain them: the New Zealand mathematician Roy Kerr, who gave us the full solution for astrophysical black holes in 1963 but has largely shunned the limelight ever since.

Melia’s book is a lively journey through the golden age of black-hole mathematics, concentrating on Kerr as one of the era’s lesser-known heroes. It was Kerr who solved Einstein’s field equations of general relativity for rotating objects, and hence successfully described how space warps around such bodies. This was a key advance, as the existing Schwarzschild and Reissner–Nordstrom solutions – discovered almost 50 years earlier – had only described bodies that were spherically symmetric, and hence had zero angular momentum. Such assumptions cannot be true for any object in the universe, so before Kerr’s breakthrough many physicists were sceptical about general relativity’s applicability to “real” astrophysical objects. It was Kerr’s important generalization that paved the way for scientists to accept the possibility of black holes, once observational evidence for their existence began to emerge in the 1960s and 1970s.

The book gets off to a bit of a rocky start, when for some reason Melia asserts that Zeno’s arrow paradox – which amounts to “how can an arrow move when snapshots show it standing still?” – requires special-relativistic principles to resolve. Although some philosophers continue to push this as a mystery, to me Aristotle’s answer is perfectly reasonable: during a very short time an arrow moves a very short distance, but it is not stationary, and if you add up the short distances over short times you get motion. Melia’s arguments to the contrary make an odd diversion, but fortunately this does not affect the rest of the book.

After this initial hiccup, Melia takes us on a quick and well-written tour of general relativity, including a good discussion of the often-overlooked contributions of Emmy Noether. This is a well-paced section, and my only suggestion would have been to include a little bit about Wallace Campbell’s eclipse expedition to Australia in 1922. Melia properly discusses Arthur Eddington’s better-known 1919 expedition, which made Einstein a star, but it was Campbell’s later observations that truly clinched the case for the light-deflection predictions. Overall, however, this is an excellent overview chapter, spanning the time between Einstein’s first attempts at a theory of gravity and the expected detection of gravitational waves within a few years from now.

The heart of the book begins in the fifth chapter, “An unbreakable code”, in which Melia gives the reader a feel for the state of general relativity in the early 1960s. At that time, it was widely viewed as an extremely complicated theory; and with only a handful of experimental confirmations, it did not attract many people to work on its intricacies. Its intrinsic mathematical beauty, however, proved sufficient to persuade a select few to seek solutions to Einstein’s nonlinear field equations. One of those was Kerr, then newly arrived at the University of Texas at Austin.

It was at this point in the text that I became most interested in what Melia had to say – particularly because Kerr (now retired and living in his native New Zealand, where he spent most of his career) has lent his support to this book in the form of an afterword. I work professionally on astrophysical applications of general relativity, and am therefore familiar with Kerr’s solution, but I knew virtually nothing about the man himself.

Melia’s portrait reveals a gifted but modest man who is deeply interested in the solutions to problems but (to his occasional detriment) not particularly concerned about getting credit for the solutions or even publishing them. Melia also offers a number of warm anecdotes about Kerr’s early career; for example, in 1951 Kerr scored a disappointing 298/600 in the mathematics portion of a scholarship exam for the University of New Zealand (now the University of Canterbury). It turns out, however, that this happened because he received a nearly perfect score on the first of the two required mathematics papers, but a zero on the second because he mistakenly turned up in the afternoon for a morning exam!

The pursuit of the Kerr solution itself is described with verve, and should be accessible and informative to specialists and non-specialists alike. I was unaware, for example, that Kerr was initially dissuaded from attempting to formulate a solution because others told him that they were hot on the trail. The ranks of “others” included Ted Newman of the University of Pittsburgh, who later modified Kerr’s solutions to account for electrically charged bodies. At one point in the pursuit, Newman thought he had proved that solutions of the desired type did not exist. When Kerr discovered a mistake in Newman’s proof, he worked full-bore to find them, using numerous elegant techniques that were not described in his eventual one-and-a-half page paper.

The fact that general relativity was something of a backwater at the time meant that few physicists and astronomers realized the magnitude of Kerr’s accomplishment. One who did was the great Indian astrophysicist Subrahmanyan Chandrasekhar, who shared the 1983 Nobel Prize for Physics and who wrote that the revelation of the Kerr solution was “the most shattering experience” of his entire scientific life. Gradually, other astronomers came to appreciate the full extent of Kerr’s legacy: simply put, the Kerr solution describes all astrophysical black holes, the only properties of which are mass and angular momentum. These are thus the simplest macroscopic objects in the universe, and the only creatures in the astrophysical zoo that can be described with mathematical exactness.

During their brief history, black holes have gone from being a dream in the 1960s to being broadly accepted by most in the 1980s. More recently, researchers have come to understand that supermassive black holes exist in most galaxies, and may play a crucial role galactic development and in the evolution of vast galaxy clusters. Melia, himself an astrophysicist at the University of Arizona, describes this progression well. He also adds a human touch by discussing Kerr’s life post-discovery, and offers a tantalizing sketch of the vistas that still await us in the study of black holes.

At 150 pages, Cracking the Einstein Code is a quick and invigorating read. It presents a lively and personal account of a subject that is a perennial favourite, and of a man who deserves more recognition. I recommend it for both scientists and anyone interested in the frustration and triumph that mark the course of scientific progress.