The Little Book of Black Holes by Steven S. Gubser and Frans Pretorious


Reviewed by Ian Lipke

Steven S. Gubser and Frans Pretorious are professors of physics at Princeton University and the authors of The Little Book of String Theory (Princeton). In the initial chapters of their ‘black holes’ volume they introduce their readers to a crash course in special and general relativity at a level that is sufficient for most readers to absorb and apply. First published in 2017, The Little Book of Black Holes is a tour de force in which the authors not only equip the novice scientist with a host of new material, but also reveal the mysteries of these phenomena in an insightful and exciting way.

Could anything be more thrilling than to be present when instrumentation dedicated to listening to the universe delivers a result which, after months of analysis, turns out to be the sound of two massive black holes coalescing a billion years ago? Three solar masses’ worth of energy originating within the black holes vaporised into gravitational radiation. But we’re talking about black holes and gravitational waves as though all of the book’s readers know what these phenomena are. In this regard the authors are most helpful.

Black holes are described as astro-physical objects and theoretical laboratories that “hone our understanding not just of gravity but also of quantum mechanics and thermal physics” (Preface ix). The message is that these constitute a very large field of knowledge. The book explains special and general relativity and then discusses Schwarschild black holes, rotating black holes, black hole collisions, gravitational radiation, Hawking radiation, and information loss. Because the knowledge field is so vast it requires light hands on the communication’s tiller if the authors are to retain their audience to the end. Fortunately, these writers acquit themselves very well. Their subject becomes accessible because the authors make extensive use of creative thought experiments and analogies to supply the concepts they are discussing. One example of this is the brilliant, upbeat letter to Einstein at the end of the book. The authors write: “The Milky Way harbours a black hole at its centre which contains about a million solar masses. We’re not pulling your leg!…We haven’t got flying cars yet, but lasers are pretty nifty” (171).

Special relativity is discussed with reference to Schwarzschild black holes in the context of objects moving relative to one another. It is of great interest but pales in significance when broadened into general relativity. The authors describe how gravity distorts Minkowski spacetime into a curved spacetime geometry. They show that matter tells spacetime how to curve. General relativity introduces the idea of fields in Einstein’s equations, from which a number of oddball ideas are derived. Einstein’s fields are identical with the curvature of spacetime, and, with general relativity scientists can describe massive objects in terms of pure geometry. “These purely geometrical massive objects are black holes” (19). It took the 1960s and 1970s to discover that a geometrical concept had flesh and bone and physical reality itself. Einstein understood that black holes were mathematical solutions to his equations, but he never accepted their physical reality. This was to change. How black holes behave and affect their surroundings are of more interest, and contain more dramatic moments, than a Stephen King thriller.

The language used in telling the story of black holes is precise and informative, encouraging and good-humoured. It is assisted by many diagrams that show with extreme clarity what the concept under discussion really means. Diagrammatic representation makes the book a valuable piece of writing.

As one would expect, the research reported here is up to date. Work on quasars and X-Ray binary star systems attributes the properties of these phenomena to the presence of black holes. That’s relatively new! Then there is the concept of entanglement with its curious effect on entropy. “If two systems are entangled, then their joint quantum state may be known precisely, in which case they have no entropy at all as a whole; and yet each system by itself may have considerable entropy” (163). There’s a puzzler! Then there is the question of how knowing a star’s surface luminosity and temperature tells us what its mass is (102). Think about that, it’s dense. While on the subject of dense as in complicated, thought, the authors have a fiendishly difficult discussion about Cyg X-1 and its invisible neighbour who must be a black hole. The point’s been made.

The physics related to black holes is presented succinctly and with due scholarship, but the upbeat attitude of the authors, most evident in the last paragraph of their letter to Einstein, sticks in my memory. Check it out for yourself.

An excellent book. Highly recommended.


The Little Book of Black Holes


By Steven S. Gubser and Frans Pretorius

Princeton UP

ISBN: 978-0-691-16372-7

$19.95; 200 pp (hardcover)



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