*The Little Book of Black Holes*approaches black holes from the perspective of fundamental physics rather than of astronomy. It also stays close to the science, with only incidental historical and biographical material; it is aimed at general readers, but will probably be enjoyed most by those with a bit of physics background.

So the opening chapter on Special Relativity appeals to intuitions from Maxwell's equations; it also gives an informal derivation of E=mc² involving light-pulses travelling between mirrors, something I had never seen before. And equations are largely eschewed, but chapter two, introducing General Relativity, gives the Einstein field equation in tensor form: "The subscripted Greek letters μ and ν are the hallmarks of so-called tensor notation, which enables us to write the ten separate field equations all at once".

On the other hand, even students of physics may find something to mull over. Chapters three and four attempt to give a feel for what happens near black holes, considering first the non-rotating Schwarzschild black hole and then the Kerr solution for a rotating black hole. There is no mathematics here, with an entirely qualitative approach explaining what different observers see, but this is still difficult to wrap one's head around, testing our intuitions for curved space.

Chapter five, "Black Holes in the Universe", then explains how observations, along with "a long chain of theoretical arguments", can be used to deduce the mass of astronomical bodies such as Cyg X-1 and make their identification as black holes plausible. This leads naturally to chapter six, "Black Hole Collisions", which looks at gravitational wave detectors such as LIGO, numerical simulation of the Einstein field equations, and how an inspiral-and-merge black hole collision might work. Under the broad heading of "Thermodynamics", chapter seven then considers quantum entanglement, entropy, the Unruh temperature, and Hawking radiation.

*The Little Book of Black Holes* is a lot of fun. I don't think I'd
recommend it to someone who had never encountered special relativity
before, but otherwise a broad range of readers should enjoy it.

November 2017

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