Introduction to General Relativity, Black Holes, and Cosmology

This is an open access title. It is made available under a Creative Commons Attribution-Non Commercial-No Derivatives 4.0 International licence. It is available to read and download as a PDF version on the Oxford Academic platform.
General Relativity is a beautiful geometric theory, simple in its mathematical formulation but leading to numerous consequences with striking physical interpretations: gravitational waves, black holes, cosmological models, and so on.
This introductory textbook is written for mathematics students interested in physics and physics students interested in exact mathematical formulations (or for anyone with a scientific mind who is curious to know more of the world we live in), recent remarkable experimental and observational results which confirm the theory are clearly described and no specialised physics knowledge is required. The mathematical level of Part A is aimed at undergraduate students and could be the basis for a course on General Relativity. Part B is more advanced, but still does not require sophisticated mathematics.
Based on Yvonne Choquet-Bruhat's more advanced text, General Relativity and the Einstein Equations, the aim of this book is to give with precision, but as simply as possible, the foundations and main consequences of General Relativity. The first five chapters from General Relativity and the Einstein Equations have been updated with new sections and chapters on black holes, gravitational waves, singularities, and the Reissner-Nordström and interior Schwarzchild solutions.
The rigour behind this book will provide readers with the perfect preparation to follow the great mathematical progress in the actual development, as well as the ability to model, the latest astrophysical and cosmological observations. The book presents basic General Relativity and provides a basis for understanding and using the fundamental theory.

Yvonne Choquet-Bruhat has worked on General Relativity (and other subjects in mathematics and physics) for some sixty years, publishing over 300 scientific papers (the most recent in July 2011). She was elected President of the International Society of General Relativity between 1980 and 1983, was the first woman to be elected to the French Academy of Sciences, is a member of the Academy of Arts and Sciences in Boston, and an elected honorary member of both the Moscow and London Mathematical Societies. She is a recipient of the Danie Heineman Prize of the American Physical Society and of the Marcel Grossman prize. Professor Emeritus of the University of Paris she is also a permanent visitor of the l'institut des hautes études scientifiques.