Curvature of space and time, with an introduction to geometric analysis
Iva Stavrov (Author)
This book introduces advanced undergraduates to Riemannian geometry and mathematical general relativity. The overall strategy of the book is to explain the concept of curvature via the Jacobi equation which, through discussion of tidal forces, further helps motivate the Einstein field equations.After addressing concepts in geometry such as metrics, covariant differentiation, tensor calculus and curvature, the book explains the mathematical framework for both special and general relativity. Relativistic concepts discussed include (initial value formulation of) the Einstein equations, stress-energy tensor, Schwarzschild space-time, ADM mass and geodesic incompleteness. The concluding chapters of the book introduce the reader to geometric analysis: original results of the author and her undergraduate student collaborators illustrate how methods of analysis and differential equations are used in addressing questions from geometry and relativity. The book is mostly self-contained and the reader is only expected to have a solid foundation in multivariable and vector calculus and linear algebra
eBook,English, 2020
American Mathematical Society ; Institute for Advanced Study, [Providence, Rhode Island], [Princeton, New Jersey], 2020
Student mathematical library, v. 93, v.93
1 online resource (xi, 243 pages) : illustrations.
9781470463137, 147046313X
1202475208
Introduction to Riemannian geometry
Differential calculus with tensors
Curvature
General relativity
Introduction to geometric analysis