When I was 8 years old, I saw a picture of the Andromeda galaxy in a children’s astronomy book. At the time I didn’t really understand what it was except that it was very big, very beautiful and a long way away. In those distant days, the night-time streetlights were not nearly as intense as they are now. And so it was that on the next dark night, armed with my newly purchased star map, I went in search of Andromeda. It didn’t look like the picture at all, it looked more like a faint bit of fluff, but I was quite certain I had located it. I reached for my Eveready torch. I carefully aimed the beam of light at Andromeda and whispered a secret message. I imagined that my message would be carried by the light all the way to Andromeda. Thus began an interest that has never waned. With age came education and a modest amount of wisdom, together with a desire to learn more about nature’s mysteries, be they on or near our lonely planet or far beyond Andromeda. I now run a small observatory in England and still gaze in awe at the night sky.

My chosen career path as a teacher, government scientist, company director and academic took me to many different countries and cultures. Later in life I started to take an interest in relativity. As the reader will discover, general relativity is all about gravity, but its implications extend far beyond Newton’s apple falling from a tree. I found it astonishing that Einstein was able to penetrate the mysteries of the Universe in an era when Andromeda and her countless heavenly relatives were wrongly regarded as belonging to our own Milky Way galaxy. Observational astronomy was still in its infancy when Einstein put pen to paper in 1905.

My first port of call was to read popular science accounts of the subject. Almost by definition, authors of such books can only go so far before informing the reader that to go any further requires mathematical description. In my journey of discovery, I found Einstein’s Princeton lectures difficult to follow, with missing details in great abundance. I then graduated to textbooks only to find that many of these also lacked crucial details that the eager learner needs, with the reader left trying to ‘figure it out’ by constantly referring to secondary texts or, perhaps as a last resort, the internet.

Here, the learner will discover that even seasoned experts in the field often cannot agree on an answer to a straightforward query from a confused student. Answers to such queries are often so embellished with mathematical rigour that the motivated student, unless very bright, is often left none the wiser. The Swiss psychologist, Jean Piaget, was a great believer in students learning by their mistakes. But, as any schoolteacher will confirm, if too many mistakes are being made then the fun of learning tends to fade. 

This book addresses these shortcomings, with an emphasis on explanation. It should be regarded as an introduction to Einstein’s theory of general relativity. There is no question that this is a very difficult topic. Almost everything about general relativity is counter-intuitive, making it hard to leave common sense behind and instead to enter the strange world of symbols and equations. 

The book has been written with a particular audience in mind. If the reader can differentiate a polynomial or trigonometric equation, can recognise a matrix or the binomial theorem, can solve a simple differential equation, and is acquainted with elementary Euclidean geometry, then, with the help of this book and a generous amount of patience, she should be able to grasp the essentials of Einstein’s general relativity, which is really a theory of gravitation. Any significant gaps in new mathematical knowledge that are needed are addressed. I refrain as far as possible from using the kind of impenetrable narrative that is often found in mathematics books on general relativity; this can be very intimidating for the learner. The book is not for high-level mathematicians, but it does necessarily contain a lot of very detailed algebra, which looks much worse than it really is. The determined reader will discover that many algebraic terms simply cancel out. 

This work is mostly aimed at university bachelor’s degree physicists and astronomers who are taking a module in general relativity but are finding the mathematics challenging. In this sense, it should be regarded as a companion guide. Students who are considering a university module in general relativity, and who want a generous taste of the subject before committing to a challenging task, will also find this book helpful.  Whatever the background of the reader, she is advised against trying to absorb everything too quickly. One step at a time is often good practice. It took Einstein ten years to develop his field equations, so we will carefully avoid the many blind alleys that Einstein encountered. 

This is not a traditional academic textbook, embellished with many student exercises in preparation for an examination. A very different and refreshing approach is adopted. Practice in the various algebraic gymnastics is done with the emphasis on proof or verification rather than derivation; this purposely comes quite late in the narrative. This strategy is especially evident in Chapter 9, which covers Einstein’s vacuum field equations. It is here that the reader is exposed to the detailed methodology of working through the relevant equations step by step, exercising what has come before. Rather than deriving the famous Schwarzschild metric, the metric is verified as being a correct solution of the underlying equations. The author refrains from making statements such as ‘it is easy to show that such and such is zero’. Rather, the reader will discover, one step at a time, that it really is zero. The emphasis is on explanation.

By the end of the book, the reader should have a grasp of the fundamentals of general relativity, together with an appreciation of the historical timeline leading up to it. The cultural significance too is briefly addressed. After all, Einstein’s relativity was an enormous leap forward in our understanding of the Universe and, later, its origin. While Darwin stopped short of entering into any theological debate about design, Einstein’s work subsequently spawned considerable debate about the notion of a divine creator and the true nature of cause and effect. He denied dualistic notions of an intervening deity, instead embracing a feeling of awe and humility towards the grandeur of the Universe. 

I once visited the silent bush country in Pilanesberg, close to the Botswana border with South Africa. In the stillness of a moonless night, the sky was over-powering in its brilliance and majesty. Einstein once declared that the most beautiful emotion we can experience is the mysterious. I hope the reader will find this book fulfilling and that the night sky far away from city lights will take on a new meaning.

© Antony Musker 2024

Praise for Einstein’s General Relativity Explained (with essential mathematics):

‘This book is a welcome and distinctive alternative to existing texts on general relativity and succeeds in setting Einstein's theory in historical context, and in rendering the subject more accessible and the maths less daunting.’

Professor Lord Martin Rees FRS, UK Astronomer Royal, Fellow of Trinity College Cambridge and former President of the Royal Society

‘Antony Musker’s passion for the captivating world of General Relativity shines through as he guides readers through the key elements of the theory, breaking down complex ideas and helping them appreciate the beauty of Einstein’s work.’

Maria Zaretskaya, European Space Agency

‘Antony Musker is to be applauded for attempting to make Einstein’s theory of relativity - perhaps the greatest scientific achievement of the human mind - accessible to readers with a modest background in mathematics – perhaps not much more than some basic calculus.’

Professor Raymon d’Inverno, Emeritus Professor of Mathematical Sciences and author of Introducing Einstein’s Relativity

‘Einstein's General Relativity Explained is an innovative guide that helps unravel the mysterious world of one of the most brilliant thinkers in history, using language that everyone can understand. Experience the awe-inspiring legacy of Einstein in a format that makes his work accessible to all with modest mathematical ability. Antony Musker deserves commendation for writing such a brilliant book that unravels the enigma of Einstein's theory of relativity. His profound expertise and background have led him to crack the code, making this book an essential for scientific enthusiasts and admirers of Einstein's legacy. Dive into the depths of knowledge and be amazed at how his words will allow you to walk in the greatness that made Einstein a historical name in the scientific world.’

Suzie Housley, Midwest Book Review