时空与几何

“... the best book on contemporary gravitational physics for beginning graduate students to established researchers. It will remain one of the leading textbooks on gravity for years to come.”

—— Renata Kallosh, Stanford University

“Carroll brings a relaxed authority to the teaching of general relativity at the graduate level. The text is beautifully written and succeeds in linking modern mathematical formalism to physical applications.”

—— Roger Blandford, Stanford University

“This book is a gem. Carroll's course at Massachusetts Institute of Technology remains legendary and this book can be expected to spread the legend worldwide. Carroll give a clear, well-motivated, and lively development of general relativity.”

—— Alan Guth, Massachusetts Institute of Technology

“An excellent graduate text in general relativity written with an informal yet sophisticated style. It provides an efficient introduction to the gravitational physics essential for today's understanding of black holes, gravitational waves, and the universe.”

—— Jim Hartle, University of California - Santa Barbara

“I recommend the book for those who know little about GR but want to learn more; it is a useful bridge between more-qualitative or even popular introductions and more-advanced textbooks.”

—— Phillip Helbig (Source: The Observatory)

本书旨在让读者清晰明了地学习广义相对论。作者以通俗易懂且生动活泼的写作风格，对广义相对论做了全面现代式的介绍，包括弯曲时空中的量子场论。全书只需要很少的预备知识即可阅读，所用的数学知识都是现用现讲，减低了学习难度。本书从平直时空的物理学（狭义相对论）开始讲起，循序渐进深入学习微分几何和爱因斯坦方程，最后讲到令人兴奋的应用，如黑洞、引力辐射和宇宙学。

更具体地，书中第一章介绍狭义相对论和基本张量代数，并包含一个场论的简要概述。紧接着的两章引入流形和曲率，并介绍与之密切相关的物理知识，主要目标还是建立数学框架。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，这些章节都贯穿有实验结论的讨论。附录中则提供了大量的数学材料来帮助读者理解正文，而且这些附录大多本身也是独立完整的。

肖恩·卡罗尔（Sean M. Carroll）是美国加州理工学院的理论物理学家，主要从事宇宙学、场论、量子力学和引力的研究。卡罗尔博士毕业于哈佛大学，曾在麻省理工学院、加州大学圣芭芭拉分校和芝加哥大学任教。他是美国物理学会的杰出会士（APS Fellow），并曾被评为美国国家科学基金会的杰出讲师（NSF Distinguished Lecturer），他获得过古根海姆奖（Guggenheim Fellowship）和美国物理联合会的安德鲁·杰曼特奖（Andrew Gemant Award）等。卡罗尔还热衷于大众科学传播，他在TED及各种知名科普电视节目上做演说，经常在《纽约时报》《华尔街日报》《自然》《科学美国人》《新科学人》《天空与望远镜》等报刊上发表科普文章，并著有《从永恒到此刻》（From Eternity to Here: The Quest for the Ultimate Theory of Time）、《寻找希格斯粒子》（The Particle at the End of the Universe: How the Hunt for the Higgs Boson Leads Us to the Edge of a New World）、《大图景：论生命的起源、意义和宇宙本身》（The Big Picture: On the Origins of Life, Meaning, and the Universe Itself）、《隐藏的宇宙》（Something Deeply Hidden: Quantum Worlds and the Emergence of Spacetime）等科普书。

Preface

1 - Special Relativity and Flat Spacetime

2 - Manifolds

3 - Curvature

4 - Gravitation

5 - The Schwarzschild Solution

6 - More General Black Holes

7 - Perturbation Theory and Gravitational Radiation

8 - Cosmology

9 - Quantum Field Theory in Curved Spacetime

APPENDIXES

Appendix A - Maps between Manifolds

Appendix B - Diffeomorphisms and Lie Derivatives

Appendix C - Submanifolds

Appendix D - Hypersurfaces

Appendix E - Stokes's Theorem

Appendix F - Geodesic Congruences

Appendix G - Conformal Transformations

Appendix H - Conformal Diagrams

Appendix I - The Parallel Propagator

Appendix J - Noncoordinate Bases

Bibliography

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