內容簡介
Einstein的廣義相對論是現代物理的基石。它包括瞭大量講述時空的前沿話題,黑洞、重力波以及宇宙學。隨著廣義相對論越來越成為同時代物理和天文學的中心,其在本科教育中的地位也顯得尤為重要。這本全新的教材很適閤本科生作為瞭解該課程的基礎理論。物理優先、數學理論盡可能少、大量的應用實例,作者為物理學傢和對該學科感興趣的讀者自然順暢的講述瞭這門學科。
讀者對象:《引力》適用於物理專業的本科生,研究生以及對該學科感興趣的廣大讀者。
目次:(第一部分)牛頓物理和狹義相對論中的時空:引力物理;幾何作為物理;牛頓物理中的空間;時間和引力;狹義相對論原理;狹義相對論力學; (第二部分)廣義相對論的彎麯時空:引力作為幾何;彎麯時空的描述;測地綫;球形星體外的幾何;廣義相對論的太陽係檢驗;實用相對論引力;引力坍縮和黑洞;天體物理學黑洞;微小轉動;鏇轉黑洞;引力波;宇宙觀察;宇宙學模型;什麼是宇宙以及為什麼;(第三部分)Einstein方程:數學部分;麯率和Einstein方程;麯率源;引力波發射;相對論星體。
內頁插圖
目錄
Preface
PART I SPACE AND TIME IN NEWTONIAN PHYSICS AND SPECIAL RELATIVITY
1 Gravitational Physics
2 Geometry as Physics
2.1 Gravity Is Geometry
2.2 Experiments in Geometry
2.3 Different Geometries
2.4 Specifying Geometry
2.5 Coordinates and Line Element
2.6 Coordinates and Invariance
3 Space, Time, and Gravity in Newtonian Physics
3.1 Inertial Frames
3.2 The Principle of Relativity
3.3 Newtonian Gravity
3.4 Gravitational and Inertial Mass
3.5 Variational Principle for Newtonian Mechanics
4 Principles of Special Relativity
4.1 The Addition of Velocities and the Michelson-Morley Experiment
4.2 Einsteins Resolution and Its Consequences
4.3 Spacetime
4.4 Time Dilation and the Twin Paradox
4.5 Lorentz Boosts
4.6 Units
5 Special Relativistic Mechanics
5.1 Four-Vectors
5.2 Special Relativistic Kinematics
5.3 Special Relativistic Dynamics
5.4 Variational Principle for Free Particle Motion
5.5 Light Rays
5.6 Observers and Observations
PART Ⅱ THE CURVED SPACETIMES OF GENERAL RELATIVITY
6 Gravity as Geometry
6.1 Testing the Equality of Gravitational and Inertial Mass
6.2 The Equivalence Principle
6.3 Clocks in a Gravitational Field
6.4 The Global Positioning System
6.5 Spacetime Is Curved
6.6 Newtonian Gravity in Spacetime Terms
7 The Description of Curved Spacetime
7.1 Coordinates
7.2 Metric
7.3 The Summation Convention
7.4 Local Inertial Frames
7.5 Light Cones and World Lines
7.6 Length, Area, Volume, and Four-Volume for Diagon Metrics
7.7 Embedding Diagrams and Wormholes
7.8 Vectors in Curved Spacetime
7.9 Three-Dimensional Surfaces in Four-Dimensional Spacetime
8 Geodesics
8.1 The Geodesic Equation
8.2 Solving the Geodesic Equation——-Symmetries and Conservation Laws
8.3 Null Geodesics
8.4 Local Inertial Frames and Freely Falling Frames
9 The Geometry Outside a Spherical Star
9.1 Schwarzschild Geometry
9.2 The Gravitational Redshift
9.3 Particle Orbits——Precession of the Perihelion
9.4 Light Ray Orbits——The Deflection and Time Delay of Light
10 Solar System Tests of General Relativity
10.1 Gravitational Redshift
10.2 PPN Parameters
10.3 Measurements of the PPN Parametery
10.4 Measurement of the PPN Parameter B-Precession of Mercurys Perihelion
11 Relativistic Gravity in Action
11.1 Gravitational Lensing
11.2 Accretion Disks Around Compact Objects
11.3 Binary Pulsars
12 Gravitational Collapse and Black Holes
12.1 The Schwarzschild Black Hole
12.2 Collapse to a Black Hole
12.3 Kruskal-Szekeres Coordinates
12.4 Nonspherical Gravitational Collapse
13 Astrophysical Black Holes
13.1 Black Holes in X-Ray Binaries
13.2 Black Holes in Galaxy Centers
13.3 Quantum Evaporation of Black Holes——Hawking Radiation
14 A Little Rotation
14.1 Rotational Dragging of Inertial Frames
14.2 Gyroscopes in Curved Spacetime
14.3 Geodetic Precession
14.4 Spacetime Outside a Slowly Rotating Spherical Body
14.5 Gyroscopes in the Spacetime of a Slowly Rotating Body
14.6 Gyros and Freely Falling Frames
15 Rotating Black Holes
15.1 Cosmic Censorship
15.2 The Kerr Geometry
15.3 The Horizon of a Rotating Black Hole
15.4 Orbits in the Equatorial Plane
15.5 The Ergosphere
16 Gravitational Waves
16.1 A Linearized Gravitational Wave
16.2 Detecting Gravitational Waves
16.3 Gravitational Wave Polarization
16.4 Gravitational Wave Interferometers
16.5 The Energy in Gravitational Waves
17 The Universe Observed
17.1 The Composition of the Universe
17.2 The Expanding Universe
17.3 Mapping the Universe
18 Cosmological Models
18.1 Homogeneous, Isotropic Spacetimes
18.2 The Cosmological Redshift
18.3 Matter, Radiation, and Vacuum
18.4 Evolution of the Flat FRW Models
18.5 The Big Bang and Age and Size of the Universe
18.6 Spatially Curved Robertson-Walker Metrics
18.7 Dynamics of the Universe
19 Which Universe and Why?
19.1 Surveying the Universe
19.2 Explaining the Universe
PART III THE EINSTEIN EQUATION
20 A Little More Math
20.1 Vectors
20.2 Dual Vectors
20.3 Tensors
20.4 The Covariant Derivative
20.5 Freely Falling Frames Again
21 Curvature and the Einstein Equation
21.1 Tidal Gravitational Forces
21.2 Equation of Geodesic Deviation
21.3 Riemann Curvature
21.4 The Einstein Equation in Vacuum
21.5 Linearized Gravity
22 The Source of Curvature
22.1 Densities
22.2 Conservation
22.2 Conservation of Energy-Momentum
22.3 The Einstein Equation
22.4 The Newtonian Limit
23 Gravitational Wave Emission
23.1 The Linearized Einstein Equation with Sources
23.2 Solving the Wave Equation with a Source
23.3 The General Solution of Linearized Gravity
23.4 Production of Weak Gravitational Waves
23.5 Gravitational Radiation from Binary Stars
23.6 The Quadrupole Formula for the Energy Loss in Gravitational Waves
23.7 Effects of Gravitational Radiation Detected in a Binary Pulsar
23.8 Strong Source Expectations
24 Relativistic Stars
24.1 The Power of the Pauli Principle
24.2 Relativistic Hydrostatic Equilibrium
24.3 Stellar Models
24.4 Matter in Its Ground State
24.5 Stability
24.6 Bounds on the Maximum Mass of Neutron Stars
APPENDIXES
A Units
A.1 Units in General
A.2 Units Employed in this Book
B Curvature Quantities
C Curvature and the Einstein Equation
D Pedagogical Strategy
D.1 Pedagogical Principles
D.2 Organization
D.3 Constructing Courses
Bibliography
Index
前言/序言
~Einsteins relativistic theory of gravitation——general relativity——will shortly be acentury old. At its core is one of the most beautiful and revolutionary conceptionsof modem science——the idea that gravity is the geometry of four-dimensionalcurved spacetime. Together with quantum theory, general relativity is one of thetwo most profound developments of twentieth-century physics. General relativity has been accurately tested in the solar system. It underliesour understanding of the universe on the largest distance scales, and is centralto the explanation of such frontier astrophysical phenomena as gravitational col-lapse, black holes, X-ray sources, neutron stars, active galactic nuclei, gravita-tional waves, and the big bang. General relativity is the intellectual origin of manyideas in contemporary elementary particle physics and is a necessary prerequisiteto understanding theories of the unification of all forces such as string theory. An introduction to this subject, so basic, so well established, so central to sev-eral branches of physics, and so interesting to the lay public is naturally a partof the education of every undergraduate physics major. Yet teaching general rel-ativity at an undergraduate level confronts a basic problem. The logical order ofteaching this subject (as for most others) is to assemble the necessary mathemati-cal tools, motivate the basic defining equations, solve the equations, and apply thesolutions to physically interesting circumstances. Developing the tools of differ-ential geometry, introducing the Einstein equation, and solving it is an elegant andsatisfying story. But it can also be a long one, too long in fact to cover both thatand introduce the many con~~temporary applications in the time that is typicallyavailable for an introductory undergraduate course. Gravity introduces general relativity in a different order. The principles onwhich it is based are discussed at greater length in Appendix D, but essentiallythe strategy is the following: The simplest physically relevant solutions of theEinstein equation are presented first, without derivation, as spacetimes whose ob-servational consequences are to be explored by the study of the motion of testparticles and light rays in them. This brings the student to the physical phenom-ena as quickly as possible. It is the part of the subject most directly connected toclassical mechanics, and requires the minimum of new mathematical ideas. TheEinstein equation is introduced later and solved to show how these geometriesoriginate. A course for junior or senior level physics students based on these principlesand the first two parts of this book has been part of the undergraduate curriculumat the University of California, Santa Barbara for over twenty-five years. It works.~
好的,以下是一本關於愛因斯坦廣義相對論導論的圖書的簡介,該簡介旨在詳細描述該領域的核心概念和發展脈絡,但不直接引用原書的特定章節或內容: --- 書名:時空織錦的幾何學:廣義相對論原理與探索 簡介: 本書旨在為讀者構建一個清晰而深刻的框架,用以理解和掌握愛因斯坦廣義相對論這一二十世紀物理學的基石理論。我們所棲居的時空,並非牛頓力學中那個被動、絕對的背景,而是一個可以被物質和能量塑形的動態實體。廣義相對論正是對這種“物質決定時空幾何,時空幾何決定物質運動”深刻洞察的數學化錶達。 全書從宏觀概念的鋪陳齣發,逐步深入到其精妙的數學結構。我們首先迴顧狹義相對論的成就與局限,尤其是它在處理引力問題時的不足。正是這種對等效原理的探索,驅使愛因斯坦超越瞭時間和空間的絕對性,將引力場這一概念,重新詮釋為時空彎麯的體現。 一、 幾何學的重生:從歐幾裏得到黎曼 廣義相對論的數學核心在於非歐幾裏得幾何,特彆是黎曼幾何的引入。本書將詳盡介紹這些必要的數學工具,但會以物理直覺為導嚮。我們將探討什麼是流形(Manifolds),張量(Tensors)如何在不同參考係下保持其物理意義的協變性,以及度規張量(Metric Tensor)如何精確地編碼瞭時空的幾何結構——即我們所感知的“距離”和“時間間隔”。 讀者將理解,運動的物體(包括光綫)遵循的是“測地綫”(Geodesics),這是在彎麯時空中兩點間最短(或最長)的路徑,這完全取代瞭牛頓引力中的“力”的概念。我們不會僅僅停留在公式的羅列,而是深入解析為何速度、質量和動量被統一在同一張描述時空扭麯的“畫布”之上。 二、 核心方程的物理內涵:愛因斯坦場方程 全書的核心驅動力是愛因斯坦場方程——一個將物質/能量分布(由能量動量張量描述)與其産生的時空麯率(由愛因斯坦張量描述)聯係起來的微分方程組。我們將逐項解析方程的各個組成部分:裏奇張量、裏奇標量、以及宇宙學常數。 場方程的精妙之處在於其內在的張力:左邊描述“幾何如何彎麯”,右邊描述“物質如何存在”。本書將重點闡述如何從這個簡潔的張量方程中,自然而然地推導齣牛頓引力定律在弱場、低速極限下的精確迴歸,這不僅是理論自洽的標誌,也是檢驗任何新引力理論的起點。 三、 經典檢驗與宇宙學圖景 廣義相對論的偉大不僅在於其理論的優雅,更在於它對一係列經典實驗現象的驚人預言和精確解釋。我們將詳細分析三個奠基性的檢驗: 1. 水星近日點的進動: 這一微小但無法用牛頓理論解釋的現象,是廣義相對論首次取得的重大勝利。 2. 光綫的彎麯: 描述瞭光綫在太陽引力場中偏摺的角度,這一預言在1919年的日食觀測中得到瞭證實,使愛因斯坦名聲大噪。 3. 引力紅移: 解釋瞭光子在爬升或下降引力勢能井時頻率的變化,這是時空彎麯對時間流逝影響的直接體現。 此外,本書也將帶領讀者進入宏大的宇宙尺度。廣義相對論是現代宇宙學的語言。我們將探討由弗裏德曼、勒梅特等人基於場方程得齣的宇宙學模型,理解宇宙膨脹的幾何基礎,以及黑洞這一極端時空幾何結構的誕生。黑洞,作為時空被無限扭麯的終極形態,其事件視界(Event Horizon)和奇點(Singularity)的概念,將從純粹的數學解中浮現,挑戰我們對空間和時間的直覺認知。 四、 進階的探索方嚮 最後,本書將觸及廣義相對論前沿研究的一些關鍵領域,為有誌於深入探索的讀者指明方嚮: 引力波: 時空本身的漣漪。我們將討論引力波的産生機製,它們在早期理論中的預言,以及近年來通過LIGO等先進設備探測到的實際信號,這標誌著我們進入瞭“引力波天文學”的新時代。 標量-張量理論與替代性引力模型: 探討除愛因斯坦場方程之外,物理學傢為解決暗能量、暗物質等當前宇宙學難題所提齣的修正引力理論框架。 量子引力的挑戰: 簡要介紹將廣義相對論與量子場論統一所麵臨的巨大障礙,這是二十一世紀理論物理學最大的未解之謎之一。 本書力求以嚴謹而不失啓發性的筆調,引導讀者跨越數學的障礙,直達廣義相對論的物理核心。它不僅是一門關於引力的學問,更是一部關於我們如何理解宇宙結構和自身在其中位置的哲學性探索。閱讀完畢後,讀者將不再將引力視為一種神秘的“力”,而是理解為時空本身的動態屬性,一個由物質刻畫的、宏偉的幾何藝術品。