As well as a handful of corrections, this third edition includes various tweaks and changes aimed at making the material yet more accessible to the general reader. Two amendments stand out. Since first writing my book, I’ve struggled with the best way of explaining vectors and one-forms, the subject matter of the first half of chapter five. Different textbooks take different approaches, most of which IMHO are hard going for the non-specialist. I’ve now rewritten this section with the emphasis on vectors as infinitesimal displacements. Even I can sort of visualise giving a point on the manifold a tiny little nudge, and I’ve even included a diagram to make things clearer. I’ve also expanded the section on Schwarzschild geodesics in chapter nine, giving a full derivation of the radial motion equation. I’ve borrowed a couple of neat Taylor series approximations from Moore’s *A General Relativity Workbook* that allows the enthusiastic reader to model Schwarzschild orbits using just a spreadsheet. They work! Even using my old Excel 2000, I can generate the pretty flower-petal effect of a precessing orbit. The book is globally available as a paperback (ISBN 9780957389465) from Amazon and other retailers, as well as in Kindle and ePub format. Thanks to all those readers who took the trouble to give feedback and report errors.

# New gravitational wave chapter

When I originally wrote this book, I only briefly mentioned gravitational waves. Space was tight, and at the time there was only indirect evidence for their existence. On 11 February 2016, the Advanced Laser Interferometer Gravitational-Wave Observatory (LIGO) team announced they had detected gravitational waves from the merger of two black holes. The press release stated:

“For the first time, scientists have observed ripples in the fabric of spacetime called gravitational waves, arriving at the earth from a cataclysmic event in the distant universe. This confirms a major prediction of Albert Einstein’s 1915 general theory of relativity and opens an unprecedented new window onto the cosmos.”

This historic discovery warrants more coverage than my original few lines, so I have now included a short additional chapter on gravitational waves. There’s a link to this new chapter here and on the home page.

# Exciting new appendix – Riemann curvature tensor derivation!

This week saw the release of the second printing of the second edition. This new printing includes those few corrections that have come to light since the publication of the second edition in 2014. There are also a handful of minor amendments, plus an additional appendix giving a (I think, rather neat) derivation of the Riemann curvature tensor and of some of its symmetries. I’ve included this new material (a) because this tensor is central to the mathematics of curvature as it relates to general relativity, and (b) the derivations provide a further useful demonstration of covariant differentiation and index manipulation in action. There’s a link to this new appendix here and on the home page.

# Hard to read maths equations on Kindle

In response to a recent one-star Amazon review complaining that the equations are too small to read on the Kindle, I’ve now added this note to the end of the Kindle ebook’s Preface:

“In the meantime, if you intend reading the book solely on a small screen reader, I advise that you check you are happy with the legibility of the equations before committing yourself to buying the book.”

Right now I have the book open in front of me on the Kindle Paperwhite (six-inch screen). And, yes, some of the maths images are on the petite side, particularly (as the reviewer points out) the subscripts and superscripts of which, this being the mathematics of general relativity, there are an abundance. Personally, a six-inch screen is the smallest I’d feel comfortable with reading my book, and ideally I’d go for something at least an inch bigger. The root causes of this problem are (1) the necessity of formatting most of the mathematical equations as images, and (2) the inability of (some/all?) Kindle readers to allow zooming of smaller images. I look forward to the day when technology allows the straightforward publishing of ebooks with flowing, scaleable mathematical text. Until that day comes, don’t forget that Amazon offer a range of free Kindle apps to let you read Kindle books on your PC, laptop, Android tablet, iPad, Mac etc.

# Second edition now published

I’m pleased to announce that the second edition of my book has just been published. Why a new edition? Simply because, despite the most careful preparation, it was inevitable that a work of this scope and complexity would contain at least some errors, ambiguities and typos. Since the book was first published two years ago, these have been slowly accumulating in the online errata sheet. This second edition consists of the original first edition text plus all those corrections and clarifications. It’s globally available as a paperback (ISBN 9780957389458) from Amazon and other retailers, as well as in Kindle and ePub format. Thanks to all those readers who took the trouble to notify me of errors in the text.

# Mangle images – resolved (hopefully)

And now it’s time to eat a large slice of humble pie. It’s a little hard to digest, but here we go.

Up until yesterday, I was confident the Kindle book “mangled images” problem was the fault of one or two dodgy Kindle devices, not my beautiful ebook file. After all, the book looked fine both on my Kindle Paperwhite and Amazon’s Kindle for PC. Plus the constituent HTML files were good on various browsers (IE, Chrome, Firefox, Opera). So, “not my fault, gov”.

As a definitive check, I decided to buy myself the basic Kindle 6″ E Ink Display. It arrived yesterday. I was mortified to see that the diagrams (there’s about a hundred of these) were, as reported, distorted, sort of weirdly overlying each other (sometimes – this appears to be an intermittent fault). It took me several hours to get find out why. All the diagrams are in GIF format and all have a transparent background. That was the problem. When I changed the background to white, they displayed fine. I’ve now uploaded a revised Kindle book file with white background GIFs. I’ve also emailed Amazon, requesting they advise readers there is an updated version available.

Apologies to all readers who were inconvenienced by this problem.

# Mangled images in Kindle book

Out of several thousand copies sold, a few readers (five at the last count) have complained of distorted images in the Kindle book. Marcus was the first to raise this issue, on Amazon.co.uk. Neither I nor the experts at Kindle Direct Publishing Support have been able to replicate this problem, which is good news unless you are one of the unfortunate readers so affected. As I say in my final comment under Marcus’s discussion, unless further information comes to light, it seems reasonable to assume that this is an individual Kindle device problem rather that an ebook file problem.

Of course, Amazon has a seven-day return policy for books bought from the Kindle Store. If you do purchase the Kindle book, I suggest you skim through it soon after downloading to ensure the images are OK and return the book if they aren’t. If you have the time and inclination, it would also be useful to contact Kindle Customer Support to ask them to check whether there is a problem with your Kindle device.