*theoretical physicists*who are interested in black holes should simply buy this new 2019 book

**Black Hole Information and Thermodynamics (SpringerBriefs in Physics)**by Dieter Lüst (Munich, the main author) and Ward Vleeshouwers (Utrecht, a young contributor). The book is basically a set of notes of some 2017 lectures by Lüst, as recorded by Vleeshouwers.

It's a book that looks at the black holes, objects predicted by Einstein's general theory of relativity, from viewpoints that are utterly modern. The book is available as Kindle or paperback.

Right now, the Amazon rank is some 1.5 million. I think that this catastrophic ranking indicates that theoretical physics – and especially the influx of the young people – has been choked to a large extent in recent years. I know that lots of young people are curious and are worried – like the older folks among us – that the knowledge of the mankind about all "deeper topics" may decrease dramatically.

Einstein completed his general relativity in 1915-1916, black hole solutions have been around since 1917, and a self-confident understanding of the existence of black holes has been available since the 1960s, when certain detailed and modern aspects were first studied. Bekenstein-Hawking thermodynamic insights were added in the 1970s. The microscopic models that agree with those predictions have been constructed since the stringy breakthroughs of the mid 1990s.

Now, lots of textbooks have been written about the "basics of general relativity". While it used to be said that only 12 people had understood GR, it was never the case. GR is reasonably understood at least by some 100,000 people on Earth (although I think that this number is already dropping quickly, too). To understand classical GR doesn't make you an elite anymore.

However, GR itself isn't a cutting-edge insight anymore. Both Jacob Bekenstein and Stephen Hawking have died. Like Einstein or Wheeler, they already belong to the history of science. So does Polchinski and others. We should build tons of sculptures of them but we're lazy. We should at least name airports and bridges after them.

You know, there has been one or two waves – or generations worth – of new insights about black holes since the "standard black hole stuff" in textbooks of general relativity. And the book by Lüst and Vleeshouwers fills the gap. Concisely enough, it introduces you into many modern topics of black holes and their behavior within a quantum mechanical theory.

A preview of the book is available through Amazon.com. Let me just say that the book covers the Riemannian geometry and cohomology (10 pages and you're an expert!); general relativity, equivalence principle, parallel transport (five pages and you get it); Einstein's equations, Christoffel symbols, Riemann curvature, Einstein's equations...

Then it presents black hole solutions, event horizons, various coordinates to write them down, conformal compactification and Penrose causal diagrams (another 10 pages in total for everything). Those get generalized to charged and rotating black holes. Somewhere here, the transition to the really modern – but already standard and settled among researchers – stuff occurs about here. Thermodynamics and its relationship to black holes, entropy, Unruh radiation, Hawking radiation.

I say that those are settled topics. We haven't experimentally observed "the Hawking evaporation of a real black hole" yet (and we probably never will, for a macroscopic black hole) but theoretical physicists have rather good reasons to believe that these effects are unavoidable consequences of theories that have been mastered and experimentally verified through their other implications, so the existence and spectrum of the Hawking radiation – which the theorists agree about because those are straightforward, although not completely trivial, calculations – is as settled as e.g. gravitational waves or the very existence of black holes were 40 years ago.

Information loss paradox and various opinions and solutions, complementarity, firewalls. String theory, T-duality, D-branes and p-branes, various solutions, counting of microstates as the Strominger-Vafa industry. Lots of these stringy black hole topics are shown – but unlike conventional string theory books, it's the "black holes" that are meant to be the main topic here. The stringy constructions are "another level" of abstraction beyond the Hawking one. Here, not only the experimental verification is absent but we don't discuss "unique answers about the right model of Nature". There are various string vacua and black holes in them. But they're examples of consistent models of quantum gravity so you may still be sure that if people keep on doing any theoretical physics of this kind, those constructions and insights will stay with us – even if the physicists make some progress in the identification of the "right single model of quantum gravity".

But there are also some 20+ pages about the BMS charges and transformation, soft hair, and similar stuff that e.g. Strominger was working on in recent years. I am afraid that this makes the final portion of the book slightly arbitrary – but the ongoing research may always turn out to be arbitrary because we're not near the "end of science". And we never will.

At the end, 128 pages is insanely thin for this vast subject – that has been extended by all the quantum, Hawking-based, and stringy extensions. According to the old-fashioned expectations, you would need some 2,000 pages (MTW times 3-5 or something). So I think that most readers can't "get it" out of 128 pages. You may be forced to calculate and think yourself, and probably look for some other texts that will help you to really understand how it works and/or learn about the details that are "really needed" although some sketch without the details may be presented as the "core". But as a list of "topics and classes and insights" that are out there, it's a precious resource. I guess that due to the increasing amount of free reading on the Internet, similar books that are "extended tables of contents" could become increasingly useful and widespread.

Even if you won't understand anything, reading just 128 pages carefully enough is a matter of days. I believe that the "wisdom per unit time" that you absorb by reading these 128 pages is higher than... for virtually any other text I can think of in the modern world. You will know that this is a text by a research who really knows his stuff, who has done a lot of his own original research but who also follows all important things by his colleagues. So even "people who aren't trained physicists" should try to read this book and get some idea about the structure of modern insights about black holes, their basic relationships, and their relative importance.

The book was written by a German and a Dutchman which is a good enough reason to try it. Maybe it's because I am Czech – and in my homeland, we received most of the hot Italian (and sometimes French) revolutions such as the revolutions in architecture through the German distillation – I tend to think that the best, most delicious and authentic Italian pizza is one processed through some German or otherwise Central-or-Northwestern-European engineers. Similarly, our president Zeman loves vegetables – but only if it is processed through the apparatus known as the pig.

When Germans or Dutchmen master something well, and if you know that they're not lost in the equations or in something else, it just makes sense and is very usable. Such a book should be comparably widely read as Misner-Thorne-Wheeler (Gravitation, 1973) although I realize that this comparison could be exaggerated a bit. As I have repeatedly said, I am afraid that the young people's exposure to these truly "cutting-edge ideas" in physics and difficult thought in general is dropping drastically. Please, prove me wrong, buy it, read it, and enjoy it!

Only after you buy it, read it, and enjoy it, note that you may also find a nearly identical text on the arXiv (2018).

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