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Tensors, Relativity, and Cosmology
Mirjana Dalarsson, Nils Dalarsson
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.
1 Introduction Part I. TENSOR ALGEBRA 2 Notation and Systems of Numbers 3 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 Cosmology Bibliography Index