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Tables of Contents for Stars and Relativity

Chapter/Section Title

Page #

Page Count

Editors' Foreword

xi

Preface to the English Edition

xiii

Preface to the First Russian Edition

xv

I. THE THEORY OF GRAVITATION

Einstein's Gravitational Equations

3

61

The Equality of Inertial and Gravitational Mass

3

3

The Fundamental Concept of the General Theory of Relativity

6

3

Properties of Noninertial Systems

9

3

The Measurement of Spacetime Intervals

12

4

Some Formulae for Curvilinear Coordinates

16

3

Dynamic and Kinematic Quantities

19

3

Curvature of Spacetime

22

2

The Einstein Field Equations and the Equations of Motion

24

4

The Cosmological Constant

28

5

Newton's Law and Weak Gravitational Fields

33

4

The Analogue of the Zeeman Effect in the Gravitational Field of a Rotating Body

37

1

Gravitational Radiation

38

7

Gravitational Radiation from Binary Stars

45

6

Gravitational Radiation Damping

51

8

K. S. Thorne

The Detection of Gravitational Waves

59

5

K. S. Thorne

Appendix to § 1.10

62

2

Inescapability of the General Theory of Relativity (GTR) and Problems in the Theory of Gravitation

64

19

Introduction

64

1

Unified Field Theory, Geometrodynamics, and the Fundamental Mass and Length

64

2

A Flat-Space Theory of Gravity

66

2

Necessity of the Concept of Spacetime Curvature

68

3

On the Possibility of Calculating the Gravitation Constant from Elementary-Particle Theory

71

3

Quantization of Gravity

74

4

Scalar-Field Gravitation

78

5

Appendix to § 2.3

80

3

The Spherically Symmetric Gravitational Field

83

46

Introduction

83

2

The Schwarzschild Gravitational Field

85

2

The Gravitational Field inside a Star

87

2

The Radial Motion of Light Rays and of Ultrarelativistic Particles

89

4

Radial Motion of Nonrelativistic Particles

93

3

Potential Curves for Nonradial Motion

96

3

Circular Orbits

99

3

The Motion of a Relativistic Particle in a Coulomb Field

102

1

Gravitational Capture of a Nonrelativistic Particle

103

2

Motion of Ultrarelativistic Particles and of Light Rays

105

1

Particle Motion in the Schwarzschild Gravitational Field, including the Effects of Gravitational Radiation

106

4

The R- and T-Regions of Schwarzschild Spacetime

110

5

Internal Solution for a Nonstatic Sphere

115

3

The Kruskal Metric

118

11

Nonspherical Gravitational Fields

129

26

Introduction

129

1

Static Fields with Axial Symmetry

130

4

The External Fields of Rotating Bodies

134

4

The Schwarzschild Sphere in an External Quadrupole Field

138

1

The Gravitational Contraction of a Slowly Rotating Body with Small Deviations from Spherical Symmetry

139

5

What Happens to Matter after It Falls through the Event Horizon?

144

11

Appendix to § 4.5

149

6

II. THE EQUATION OF STATE OF MATTER

Introduction to Part II

155

5

The Concept of Pressure; Different Kinds of Pressure; the Case of Long-Range Interactions

155

5

Cold Matter

160

41

Classification into Domains

160

3

Degenerate Electron Gas

163

4

Corrections in the Domain of High Pressures

167

2

The Domain of Medium Densities, 106 < ρ < 500 g cm-3

169

5

Nuclear Processes and Nuclear Interactions: Their Effect upon the Equation of State

174

7

The Properties of a Neutron Gas

181

4

Density Greater than Nuclear

185

2

An Ideal Neutron Gas at Superhigh Density

187

1

Ideal Gas with the Inclusion of Reciprocal Transformations between Particles

188

5

Are All ``Elementary'' Particles Really Elementary?

193

1

The Electromagnetic Interaction of Particles

194

3

A Rigorous Limit upon the Equation of State?

197

4

Properties of Matter at High Temperatures

201

10

Physical Conditions in Ordinary Stars

201

1

High Temperatures

202

3

Various Types of Equilibrium

205

6

Thermodynamic Quantities at High Temperatures

211

22

Neutral Gas, Plasma; Ionization Equilibrium

211

3

The Thermodynamics of Radiation

214

3

Paris and Neutrinos

217

4

The Dissociation of Nuclei

221

4

Dense Matter at Low Temperatures

225

1

Dimensionless Entropy

226

2

General Thermodynamic Relations for Truly Neutral Matter

228

5

III. RELATIVISTIC STAGES OF EVOLUTION OF COSMIC OBJECTS

Introduction to Part III

233

6

The Equilibrium and Stability of Stars

239

91

The Equilibrium and Stability of a Star as a Whole

239

6

General Aspects of the Theory of Stellar Equilibrium

245

4

Analytic Theory of Polytropic Gas Spheres

249

3

The Adiabatic and Polytropic Indices

252

2

The Energy Approach to the Theory of Equilibrium for a Star Consisting of Matter with γ Close to 4/3

254

2

Relativistic Equations of Stellar Equilibrium

256

8

Relativistic Equations for Rotating Stars

264

7

K. S. Thorne

Theory of Cold White Dwarfs

271

8

Neutron Stars

279

7

The Mass Defect

286

2

Stability of Neutron Stars

288

3

Configurations with Positive Energy

291

4

The Metastability of Every Equilibrium State

295

2

Equilibrium of a Supermassive Star

297

12

Critical States of Stars with Intermediate Mass

309

21

Appendix to § 10.1

317

2

Appendix to § 10.5

319

3

Appendix 1 to § 10.8

322

1

Appendix 2 to § 10.8

322

3

Appendix 1 to § 10.14

325

3

Appendix 2 to § 10.14

328

2

Stellar Evolution

330

86

Evolution of a Star up to the Loss of Stability or the White-Dwarf Stage

330

8

Instability of Massive Stars with Nuclear Sources of Energy

338

2

Stability of Stellar Evolution

340

5

Supernova Outbursts

345

19

V. S. Imshennik

D. K. Nadezhin

The Physics of Neutron Stars

364

5

Evolution of a Star with a Mass Greater than the Oppenheimer-Volkoff Limit

369

1

Relativistic Collapse

370

3

Neutrino Emission in the Collapse of a Cool Star

373

3

The Evolution of a Supermassive Star: General Remarks

376

1

Radiative Equilibrium

377

2

The Evolution of a Supermassive Star without Turbulence or Rotation

379

5

Rotation and Mass Shedding: General Relationships

384

5

Equilibrium and the Shape of a Rotating Star: The Newtonian Theory

389

4

Corrections for GTR in the Theory of a Rotating Star

393

5

Approximate Theory of Equilibrium

398

2

Rotating Massive Stars and Quasistellar Objects

400

3

Turbulence

403

2

The Evolution of a Rotating Star: Velocity of Mass Ejection

405

11

Appendix to § 11.11D

410

6

Star Clusters

416

16

General Overview and Basic Equations

416

5

Solutions for Nonrelativistic Star Clusters

421

3

The Stability of Collisionless Solutions

424

2

Physical Conditions, Collisions, and Evolution in Star Clusters

426

2

Relativistic Star Clusters

428

4

Physical Processes in the Vicinities of Relativistic Objects and a Comparison with Observations

432

41

Accretion of Gas by Neutron Stars and Collapsed Stars

432

1

The Infall of Noninteracting Particles

433

2

Four Regimes of Hydrodynamical Flow in the Case of Spherical Symmetry

435

3

The Case of Accretion and the Validity of the Hydrodynamical Approximation

438

4

The Luminosity due to Symmetric Accretion onto Neutron Stars and White Dwarfs

442

2

The Problem of Discovering Collapsed Stars

444

2

The Case of Asymmetric Gas Flow

446

5

Accretion as a Factor in Stellar Evolution

451

1

The Electrostatic Field, Acceleration of Positrons during Accretion, and Gamma-Ray Emission

451

1

Pulsars

452

5

The Superfluidity and Superconductivity of Highly Compressed Matter, and Their Influence on the Behavior of Neutron Stars

457

2

Magnetic and Magneohydrodynamic Phenomena in Collapsing Bodies

459

5

The Statistics of Stars at the Endpoint of Stellar Evolution

464

9

Quasistellar Objects

473

12

Observed Properties of Quasistellar Objects

473

3

Theories of Quasistellar Objects

476

9

References

485

26

Author Index

511

5

Subject Index

516