The book is a comprehensive introduction to general relativity, black holes, and cosmology, written by a renowned mathematician. It is praised for its mathematical rigor and deep understanding of both physics and mathematics, but may not be suitable as a first book for physics students due to its mathematical focus.
The book 'Introduction to General Relativity, Black Holes, and Cosmology' by Yvonne Choquet-Bruhat is a two-part text covering 'Fundamentals' and 'Advanced Topics'. It starts with the mathematics of differential geometry, explaining manifolds, tensor fields, metrics, connections, and curvature. The book then moves on to the flat metric of special relativity, the curved metrics of general relativity, and the Einstein field equations. The applications of general relativity to black holes and cosmology are also discussed, including the Schwarzschild and Kerr metrics, and the symmetries of cosmological metrics. The 'Advanced Topics' section focuses on the Cauchy problem for the Einstein field equations, both without matter and with various types of matter. While the book is highly regarded for its mathematical rigor and deep understanding of both physics and mathematics, it may not be suitable as a first book for physics students due to its mathematical focus. It is, however, an ideal introduction to the mathematical approach for those who already know some general relativity.
Quick quotes
The book provides an elementary introduction to the physics of general relativity and a beautiful exposition of how that physics relates to the differential geometry of spacetime and to the hyperbolic nonlinear partial differential equations that describe the evolution of the gravitational field.
However, I would not recommend it as a first book in general relativity for a physicist.
For a reader who already knows some general relativity, Choquet-Bruhat’s book is an ideal introduction to the mathematical approach.