章节目录
1 Special Relativity and Flat Spacetime 1.1 Prelude 1.2 Space and Time, Separately and Together 1.3 Lorentz Transformations 1.4 Vectors 1.5 Dual Vectors (One-Forms) 1.6 Tensors 1.7 Manipulating Tensors 1.8 Maxwell's Equations 1.9 Energy and Momentum 1.10 Classical Field Theory 1.11 Exercises 2 Manifolds 2.1 Gravity as Geometry 2.2 What Is a Manifold? 2.3 Vectors Again 2.4 Tensors Again 2.5 The Metric 2.6 An Expanding Universe 2.7 Causality 2.8 Tensor Densities 2.9 Differential Forms 2.10 Integration 2.11 Exercises 3 Curvature 3.1 Overview 3.2 Covariant Derivatives 3.3 Parallel Transport and Geodesics 3.4 Properties of Geodesics 3.5 The Expanding Universe Revisited 3.6 The Riemann Curvature Tensor 3.7 Properties of the Riemann Tensor 3.8 Symmetries and Killing Vectors 3.9 Maximally Symmetric Spaces 3.10 Geodesic Deviation 3.11 Exercises 4 Gravitation 4.1 Physics in Curved Spacetime 4.2 Einstein's Equation 4.3 Lagrangian Formulation 4.4 Properties of Einstein's Equation 4.5 The Cosmological Constant 4.6 Energy Conditions 4.7 The Equivalence Principle Revisited 4.8 Alternative Theories 4.9 Exercises 5 The Schwarzschild Solution 5.1 The Schwarzschild Metric 5.2 Birkhoff's Theorem 5.3 Singularities 5.4 Geodesics of Schwarzschild 5.5 Experimental Tests 5.6 Schwarzschild Black Holes 5.7 The Maximally Extended Schwarzschild Solution 5.8 Stars and Black Holes 5.9 Exercises 6 More General Black Holes 6.1 The Black Hole Zoo 6.2 Event Horizons 6.3 Killing Horizons 6.4 Mass, Charge, and Spin 6.5 Charged (Reissner-Nordstrom) Black Holes 6.6 Rotating (Kerr) Black Holes 6.7 The Penrose Process and Black-Hole Thermodynamics 6.8 Exercises 7 Perturbation Theory and Gravitational Radiation 8 Cosmology 9 Quantum Field Theory in Curved Spacetime APPENDIXES Bibliography Index
内容简介
这本书旨在让读者清晰明了地接触广义相对论，广义相对论的引入，从大爆炸到黑洞，这样很容易激起读者对物理学的浓厚兴趣。附录中提供了大量的数学材料来帮助读者理解正文，而且附录的很多部分本身也是独立完整的。 本书的结构，第一章主要介绍狭义相对论和基本张量代数，包含一个场论的简要概述。紧接着的两章引入流形和曲率，包含一些具有激发性的物理知识，但主要目标是建立数学框架。第四章引入广义相对论，并且给出一些择一性定理的讨论。紧接着的四章主要讨论广义相对论的三大主要用途：黑洞，扰动理论和引力波，以及宇宙学。这些章节都贯穿有试验性结论的讨论，使得这些理论的实用性马上显现出来。 本书很适合物理系高年级本科生、研究生以及对广义相对论感兴趣的读者。 注：本书为全英文版。
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