Tensors, Relativity, and Cosmology

By

  • Mirjana Dalarsson, MSc – Engineering Physics 1984 Licentiate – Engineering Physics 1989, Ericsson Research and Development, Stockholm, Sweden
  • Nils Dalarsson, MSc – Engineering Physics 1982 Licentiate (Swedish degree between MSc and PhD) – Theoretical Physics 1990 PhD – Theoretical Physics 1993 MBA – Mathematical Finance 1998 MSc – Education 2012 , Royal Institute of Technology, Department of Theoretical Physics, Stockholm, Sweden
  • Mirjana Dalarsson, MSc – Engineering Physics 1984 Licentiate – Engineering Physics 1989, Ericsson Research and Development, Stockholm, Sweden

This book combines relativity, astrophysics, and cosmology in a single volume, providing an introduction to each subject that enables students to understand more detailed treatises as well as the current literature. The section on general relativity gives the case for a curved space-time, presents the mathematical background (tensor calculus, Riemannian geometry), discusses the Einstein equation and its solutions (including black holes, Penrose processes, and similar topics), and considers the energy-momentum tensor for various solutions. The next section on relativistic astrophysics discusses stellar contraction and collapse, neutron stars and their equations of state, black holes, and accretion onto collapsed objects. Lastly, the section on cosmology discusses various cosmological models, observational tests, and scenarios for the early universe.
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Audience

Upper undergraduate and graduate students in physics and cosmology.

 

Book information

  • Published: March 2005
  • Imprint: ACADEMIC PRESS
  • ISBN: 978-0-12-200681-4

Reviews

"…it’s absolutely perfect if you need help with the mathematical aspects of relativity…Many notions from tensor algebra and differential geometry are introduced and explained very clearly, and the main essential formulas are all presented in details."--BookInspections.com, May 27, 2013




Table of Contents

1 Introduction Part I. TENSOR ALGEBRA 2 Notation and Systems of Numbers3 Vector Spaces 4 Definitions of Tensors 5 Relative Tensors 6 The Metric Tensor 7 Tensors as Linear Operators Part II. TENSOR ANALYSIS 8 Tensor Derivatives 9 Christoffel Symbols 10 Differential Operators 11 Geodesic Lines 12 The Curvature Tensor Part III. SPECIAL THEORY OF RELATIVITY 13 Relativistic Kinematics 14 Relativistic Dynamics 15 Electromagnetic Fields 16 Electromagnetic Field Equations Part IV. GENERAL THEORY OF RELATIVITY 17 Gravitational Fields 18 Gravitational Field Equations 19 Solutions of Field Equations 20 Applications of Schwarzschild Metric Part V ELEMENTS OF COSMOLOGY 21 The Robertson-Walker Metric 22 The Cosmic Dynamics 23 Non-static Models of the Universe 24 The Quantum CosmologyBibliography Index