Curvature of space and time, with an introduction to geometric analysis / Iva Stavrov.

Format:

Book

Author/Creator:

Stavrov, Iva, 1976- author.

Series:

Student mathematical library ; v. 93.

Student mathematical library. IAS/Park City mathematical subseries.

Student mathematical library. IAS/Park City mathematical subseries

Student mathematical library ; volume 93

Language:

English

Subjects (All):

General relativity (Physics)--Mathematics.

General relativity (Physics).

Space and time.

Geometry, Riemannian.

Geometry, Differential.

Geometric analysis.

Curvature.

Physical Description:

1 online resource (xi, 243 pages) : illustrations.

Edition:

1st ed.

Place of Publication:

Providence, Rhode Island : American Mathematical Society ; Princeton, New Jersey : Institute for Advanced Study, [2020]

Summary:

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.The material in this book was first developed for the 2013 summer program in geometric analysis at the Park City Math Institute, and was recently modified and expanded to reflect the author's experience of teaching mathematical general relativity to advanced undergraduates at Lewis & Clark College.

Contents:

Introduction to Riemannian geometry

Differential calculus with tensors

Curvature

General relativity

Introduction to geometric analysis.

Notes:

Includes bibliographical references and index.

Description based on online resource; title from digital table of contents page (viewed on April 22, 2021)

Description based on publisher supplied metadata and other sources.

ISBN:

1-4704-6313-X

OCLC:

1202475208