What is a good introduction to general relativity for a mathematician?
A direct and specific Quora question. Definitely demands a direct and specific answer 🙂
It’s an old book, but still very readable as an introduction for mathematicians. And the author is Hermann Weyl, out of all people. And I personally like him even more since he also graduated from the University of Göttingen.
And then, of course, you have the all-time classics L.D. Landau & E.M. Lifshitz “The Classical Theory of Fields” ( Volume 2 of A Course of Theoretical Physics ).
Yes, these are the guys from the Landau-Lifshitz equation. Landau was a Nobel Prize winner (and a student at Göttingen 🙂 ), and both Landau and Evgeny Lifshitz were academicians of the Russian Academy of Sciences and honorary members of many other national scientific societies around the globe.
Their book is rough, tough and mathematical, but provides a great introduction and explains so many important aspects of the theory, while most of modern introductory books just do hand waving and popular lingo speaking for hundreds of pages.
And, as a note of caution: if you aim to understand the general relativity and do not want to read pseudo-scientific fantasy, avoid books by Stephen Hawking.
P.S. The guy from the picture above is famous not only for his creation of the relativity theory, but also for some of the work that he did at the German Federal Institute of Physical and Technical Affairs, also known as PTB and as the place where I’m happily doing my own research affairs for the past three years. The world feels so small right now 🙂