Non-Fiction Reviews

Black Holes
A Very Short Introduction

(2015) Katherine Blundell, Oxford University Press, 7.99, pbk, xix + 100 pp, ISBN 978-0-199-60266-7


The Oxford Very Short Introductions series began in 1995 and now contains over 400 volumes on a wide range of topics, 'for anyone wanting a stimulating and accessible way into a new subject. They are written by experts, and have been translated into more than 40 different languages'. The books are compact, lightweight, and an easy fit even for quite a small pocket but the print size is small and the paper, though strong, is thin, so this supposedly short book is a quite comprehensive introduction to black holes.

As promised the writing is accessible and the esoteric topics come with simple analogies to illuminate what's going to be put across. Occasionally in my view the wording becomes too casual, as when 'the Andromeda galaxy' is introduced without giving its full name, the Great Galaxy in Andromeda. I can understand why for simplicity the author chose not to use the unequivocal 'M31', requiring an explanation of Messier numbers. But the text goes on to discuss events 'on' Andromeda as if it is a planet, rather than a galaxy within a particular constellation. It is a minor point, but for readers who require those simple explanations of basic points, a detail like that might cause confusion.

Nevertheless I was enjoying the clear account of the more complex matters, so much so that I was hoping for clarification of one aspect of black hole theory which particularly bugs me, concerning how, to an outside observer, a spacecraft which fell into one would appear to be 'frozen' at the event horizon. I understand how such an appearance might be generated for an observer who was located exactly on the line of flight, but to one at 90 degrees from it, the standard account appears to generate a relativistic version of Xeno's Paradox. To my disappointment Katherine Blundell doesn't clear up what I take to be my own confusion on this point: she only describes how the experience of an observer on the spacecraft would be different. One aspect of that is the process of 'spaghettification', where the spacecraft and the observer would be stretched to destruction by tidal forces on the approach to the event horizon. But there's no mention (here or anywhere else that I've read of this) of how Fitzgerald contraction would affect that, either as witnessed by the outside observer or on the spacecraft itself? It appears to me to generate another paradox, especially if the event is viewed from off the direct flight path, as it would have to be on any approach to a rotating black hole Blundell makes that point very clear.

But at that point I hit real trouble, with a statement that on the approach to a spinning black hole, frame dragging would force the falling spacecraft to start 'orbiting' it. I can see that the path of its fall would change to a spiral, but even in a rotating space-time frame, to achieve orbit would surely need lateral thrust. The next section is headed 'Orbiting around a black hole' and it's about the behaviour of photons within the volume of space which frame dagging affects. Now, it may be a blind spot due to the grounding in astrodynamics which I had from the late Prof. Archie Roy, but if escape velocity at the event horizon is the speed of light, then something in orbit at some distance above it surely must be travelling at less than that speed and a photon, by definition, cannot do that. Frame dragging complicates the issue, but not that much at the event horizon space-time rotates with it (page 30), and the fastest-known rotating black hole, discovered only weeks ago, is spinning at only one-third of lightspeed.  Then Blundell started talking about the behaviour of photons orbiting at a distance of half the Schwarzchild radius that would be inside the event horizon, as defined on page 5, and it's made clear, soon after, that nothing can be said about what happens in there. I think that Blundell is writing 'orbital radius' where she means orbital altitude, i.e. distance above the event horizon, and I think she is using 'orbital' here to mean circular motion, as one might speak of an aircraft orbiting a beacon. With those substitutions, the final pages of Chapter 4 appear to make sense to me but the process described is so complex that I can't be entirely sure.

In A.G.W. Cameron's 1963 anthology Interstellar Communication, Freeman Dyson published a paper, 'Gravitational Machines', explaining how an advanced civilisation could use a variant of gravitational slingshot to extract energy from a binary star system, ending with a prediction of the exact mechanism by which the gravitational waves which have now been detected, would be produced by the decay of a binary comprising two neutron stars. His 'machine' could be used to launch spacecraft at high fractions of lightspeed, or, by capturing them with electromagnetic braking, very large amounts of power could be obtained. Roger Penrose later pointed out that still more energy could be obtained by close passage around a black hole. This is mentioned in Chapter 3, where the reader is promised a fuller account in Chapter 7, but actually there's only a slightly expanded one in Chapter 5. What we get in Chapter 7 is an account of how matter in an accretion disc around a black hole is heated to plasma temperatures as it spirals inwards, losing energy in collisions. A great deal of radiant energy is released and an advanced civilisation could tap that using solar panels or parabolic collectors (Sydney Jordan's Lance McLane comic strip in the 1970s and 80s featured a civilisation at Epsilon Aurigae doing just that, when the star's companion was thought to be a black hole). But although the diagram on p.67 correctly shows that potential energy is being converted to kinetic energy and then through collisions into heat, Blundell describes it as nuclear energy, writing 'The energy that is available to be radiated out is the difference between the energy the infalling mass has far away before it is accelerated (calculated using Einstein's famous formula E = mc², where E is energy, m is mass and c is the speed of light.) and the energy it has at the innermost stable circular orbit of the black hole.'  Actually, I would have thought that the available energy is proportional to ½ mv1² - ½ mv0², which is still a very respectable quantity in this situation, but a lot less than mc² would be.

To repeat, these are minor issues in an otherwise excellent book; the pages complained of are only 7 out of 93 pages of text, plus further recommended reading and index.  For whom this book is intended is a more difficult question. Personally, I shall keep the book on top of my astrophysics shelf so that I can use it for quick reference when (say) I need to remind myself of the difference between the photon sphere, the ergosphere and the static sphere, all of them stressed regions of space-time near an event horizon, but with different definitions and properties.  But for all the book's compactness and portability, I am not going to carry it around on a day-to-day basis. I suppose I might take it to a top-level conference, if I was afraid I would be out of my depth.  But I won't need to be reminded of the terms in E = mc², much less that Einstein's equation is famous, nor (three pages later) that electron scattering by photons simply means 'giving energy and momentum to'. Readers who need explanations of that kind probably won't notice the issues I have highlighted above, because they will struggle with a great deal more of the book.

In writing classes, I am often asked by readers who do not have a scientific background 'How can I achieve sufficient authenticity to write SF?', and like other writers, I reply that in most cases the children's section of the public library will provide what's needed, up-to-date, accurate and with the simplest explanations. With regret, I couldn't recommend this book for that purpose; but I can and will make use of it myself.

Duncan Lunan

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