The geometry of spacetime : a mathematical introduction to relativity theory / Rainer Oloff.

Format:

Book

Author/Creator:

Oloff, Rainer, author.

Series:

Graduate Texts in Physics, 1868-4521

Language:

English

Subjects (All):

Geometry, Differential.

Relativity (Physics)--Mathematics.

Relativity (Physics).

Physical Description:

1 online resource (283 pages)

Edition:

1st ed. 2023.

Place of Publication:

Cham, Switzerland : Springer Spektrum, [2018]

Summary:

This book systematically develops the mathematical foundations of the theory of relativity and links them to physical relations. For this purpose, differential geometry on manifolds is introduced first, including differentiation and integration, and special relativity is presented as tensor calculus on tangential spaces. Using Einstein's field equations relating curvature to matter, the relativistic effects in the solar system including black holes are discussed in detail. The text is aimed at students of physics and mathematics and assumes only basic knowledge of classical differential and integral calculus and linear algebra.

Contents:

Differentiable manifolds

Tangent vectors

Tensors

Semi-Riemann manifolds

Special relativity

Differential forms

Covariant derivation of vector fields

Curvature

Matter

Geodesy

Covariant differentiation of tensor fields

Lie derivation

Integration on manifolds

Non-rotating black holes

Cosmology

Rotating black holes

An overview of string theory.

Notes:

Includes bibliographical references and index.

Description based on print version record.

Other Format:

Print version: Oloff, Rainer The Geometry of Spacetime

ISBN:

9783031161391

OCLC:

1377309738