The Geometry of Spacetime

A Mathematical Introduction to Relativity Theory
2023
ISBN: 978-3-031-16141-4
Verlag: Springer Nature Switzerland

Buch, Englisch, 274 Seiten, Format (B × H): 155 mm x 235 mm, Gewicht: 452 g

Reihe: Graduate Texts in Physics

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.

Zielgruppe

Upper undergraduate

Autoren/Hrsg.

Oloff, Rainer

Fachgebiete

• Naturwissenschaften Physik Physik Allgemein Theoretische Physik, Mathematische Physik, Computerphysik
• Naturwissenschaften Physik Physik Allgemein Geschichte der Physik
• Naturwissenschaften Astronomie Kosmologie, Urknalltheorie
• Naturwissenschaften Physik Quantenphysik Relativität, Gravitation

Inhaltsverzeichnis

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.

Über Autor(innen)

Rainer Oloff received his doctorate, and later taught, at the Friedrich Schiller University of Jena, specializing in the field of analysis. He also had sojourns teaching at the Addis Ababa University and the University of Salzburg.