Compact Objects in Astrophysics: White Dwarfs, Neutron Stars and Black Holes

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Springer Science & Business Media, Feb 24, 2007 - Science - 679 pages

Compact objects are an important class of astronomical objects in current research. Supermassive black holes play an important role in the understanding of the formation of galaxies in the early Universe. Old white dwarfs are nowadays used to calibrate the age of the Universe. Mergers of neutron stars and black holes are the sources of intense gravitational waves which will be measured in the next ten years by gravitational wave detectors.

Camenzind's Compact Objects in Astrophysics gives a comprehensive introduction and up-to-date overview about the physical processes behind these objects, covering the field from the beginning to most recent results, including all relevant observations.

After a presentation of the taxonomy of compact objects, the basic principles of general relativity are given. The author then discusses in detail the physics and observations of white dwarfs and neutron stars (including the most recent equations of state for neutron star matter), the gravitational field of rapidly rotating compact objects, rotating black holes (including ray tracing and black hole magnetospheres), gravitational waves, and the new understanding of accretion processes by means of the magnetorotational instability of accretion disks.
This modern treatise of compact object astrophysics uses the 3+1 split approach to Einstein's equations, and to relativistic hydrodynamics and magnetohydrodynamics. In each chapter problems and solutions help deepen the understanding of the subject. Both advanced students and researchers will appreciate this book as an advanced textbook and reference on this fascinating field of astrophysics.

 

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Contents

71 Spacetime of Stationary and Axisymmetric Rotating Bodies
308
711 Physical Interpretation of the Metric
309
712 Geodetic and LenseThirring Precession
312
713 On General 3+1 Split of Spacetime
315
72 Einsteins Field Equations for Rotating Objects
317
721 Ricci Tensors of TimeSlices
318
722 Extrinsic Curvature and 4D Ricci Tensors
319
723 3+1 Split of Einsteins Equations
320

16 GammaRay Bursters
19
Problems
25
Gravity of Compact Objects
27
22 The Basic Principles of General Relativity
29
222 Metric Theories of Gravity
33
23 Basic Calculus on Manifolds
37
232 The Metric Field and PseudoRiemannian Manifolds
42
233 The Calculus of Forms on Lorentzian Manifolds
44
24 Affine Connection and Covariant Derivative
47
243 Covariant Derivative for Tensor Fields
48
244 Parallel Transport and Metric Connection
50
245 Metric Connection
52
246 Divergence of Vector Fields
55
25 Curvature of PseudoRiemannian Manifolds
56
251 Mathematical Definition of Torsion and Curvature
57
252 Bianchi Identities for Metric Connection
58
253 Ricci Weyl and Einstein Tensor
60
254 Cartans Structure Equations
61
26 Gravity is a Lorentzian Connection on Spacetime
65
262 The Hilbert Action and Einsteins Field Equations
68
263 On the Cosmological Constant
69
264 Limits of General Relativity
71
27 Gravitational Waves
73
272 Gravity Wave Experiments
74
273 The Nature of Gravitational Waves
76
274 Degrees of Freedom
79
275 Gravitational Wave Solutions
83
276 The Quadrupole Formula
87
28 3+1 Split of Einsteins Equations
91
281 Induced Spatial Metric and Extrinsic Curvature
92
282 Hypersurface Embedding
93
283 Split of Affine Connection and Curvature
95
284 Split of Einsteins Equations
98
285 Black Hole Simulations and Gravitational Waves
100
Problems
101
Matter Models for Compact Objects
104
311 Relativistic Plasma Equations
106
312 On Numerics of Hydrodynamics
110
32 The Boltzmann Equation in GR
113
322 Particle Number Current and EnergyMomentum Tensor
116
323 The Relativistic Boltzmann Equation
117
324 Liouville Operator in 3+1 Split
118
325 Transformation into the Local Rest Frame
119
Problems
120
Relativistic Stellar Structure
123
42 Derivation of the TOV Equations
125
422 Matter in the Interior
127
423 The Exterior Schwarzschild Solution
130
424 Stable Branches for Degenerate Stars
131
43 A Variational Principle for the Stellar Structure
132
Problems
134
White Dwarfs
137
51 Observations of Isolated White Dwarfs
138
512 Field White Dwarfs and Classification
139
513 White Dwarfs in Globular Clusters
143
515 Ultracool White Dwarfs as Cosmochronometers
145
52 What is Inside a White Dwarf?
151
53 Equation of State below the Neutron Drip Density
153
54 Structure of White Dwarfs and the Chandrasekhar Mass
159
541 Polytropic Approximation
160
542 Beyond the Chandrasekhar Treatment
162
55 The Relativistic Instability of White Dwarf Stars
167
551 Necessary Condition for Stability
168
552 The Total Energy in the PostNewtonian Limit
169
553 GR White Dwarf Instability
171
56 Cooling White Dwarfs
174
561 Structure of the Surface Layers
175
562 Cooling Curves and Crystallization
177
563 Testing WD Crystallization Theory
179
57 White Dwarfs in Binary Systems
180
Problems
185
Neutron Stars
186
61 The Structure of a Neutron Star
188
62 Equations of State beyond Neutron Drip
189
621 From Neutron Drip to Saturation
190
622 Nuclear EoS for Dense Neutron Matter
199
623 Relativistic Mean Field Theory above Saturation
206
624 Analytical Fits to EoS
216
63 Neutron Star Models
219
632 Quark Matter Cores
224
633 Grand Canonical Potential for Quark Matter
231
634 Strange Quark Stars
241
635 The Structure of Massive Neutron Stars
242
64 Neutron Stars in Close Binary Systems
244
642 Periastron Shift in TwoBody Systems
248
643 The Shapiro Time Delay in a Binary System
250
644 Decay of Binary Orbits due to Gravitational Radiation
251
65 Masses of Neutron Stars from Radio Pulsar Timing
255
652 The Timing Formula
259
653 Timing of the Binary System PSR B1913+16
263
654 Masses of Companion Stars
264
655 The Double Pulsar System PSR 07373039A+B
265
66 Neutron Stars in our Galaxy
269
662 Thermal Emission from Isolated Neutron Stars
272
663 RotationPowered Pulsars
284
664 AccretionPowered Neutron Stars and the MassRadius Relation
294
Problems
303
Rapidly Rotating Neutron Stars
307
73 Stellar Structure Equations in Isotropic Gauge
321
732 Structure Equations for Rotating Stars
322
733 Mechanical Equilibrium and Effective Potential
324
734 Stellar Parameters
326
74 The SlowRotation Approximation
332
75 Numerical Integration of the Stellar Structure Equations
335
751 Comparison of Numerical Codes
337
752 Properties of Rotating Equilibrium Stellar Structures
338
76 Towards Analytical Vacuum Solutions for Rotating Neutron Stars
342
762 Ernst Equations
343
763 Mankos Solution
345
77 On Oscillation and Formation of Rotating Neutron Stars
350
Problems
353
Black Holes
355
811 Tortoise Coordinates and Null Cones
356
812 Roads towards Black Hole Formation
358
813 The Kruskal Extension
359
814 Penrose Diagram the Conformal Structure of Infinity
363
82 Geodetic Motions in Schwarzschild Spacetime
369
822 The Effective Potential for Equatorial Motion
371
823 Orbital Equation and Bound Orbits in Schwarzschild Spacetime
373
83 The Kerr Black Hole
378
831 Kerr Black Hole in BoyerLindquist Coordinates
379
833 The WeylPapapetrou Form of the Kerr Metric
384
834 Uniqueness of the Kerr Solution
385
835 Global Properties of the Kerr Metric
386
836 On the Conformal Structure of the Kerr Solution
393
837 Ernsts Equations for the Kerr Geometry
394
838 The KerrSchild Metric and TwoBlackHole States
395
84 Rotational Energy and the Four Laws of Black Hole Evolution
399
841 Surface Gravity and Angular Velocity of the Horizon
400
842 First Law of Black Hole Dynamics
402
843 Rotational Energy of Astrophysical Black Holes
405
844 On the Second and Third Laws of Black Hole Dynamics
406
85 Time Evolution of Black Holes
408
852 Merging of Black Holes
411
86 Geodesics in the Kerr Geometry
412
861 Direct Integration of Geodesics Equations
414
862 Geodesies in the Equatorial Plane
416
863 Geodesics Including Lateral Motion
424
864 Null Geodesics and RayTracing in Kerr Geometry
431
87 Dark Energy Stars
442
872 Structure of Gravastars
443
873 The Necessity of an Anisotropic Crust
445
Problems
446
Astrophysical Black Holes
449
91 Classes of Astrophysical Black Holes
450
92 Measuring Black Hole Masses
451
922 IntermediateMass Black Holes
456
924 Black Holes in Quasars
468
93 Estimating Black Hole Spin
470
931 Black Hole Spin and Radio Galaxies
471
933 Relativistic Iron Lines
472
95 Black Hole Magnetospheres
473
951 The 3+1 Formalism for Maxwells Equations
474
952 Plasma Equations in the 3+1 Split
478
953 Time Evolution of Magnetic and Current Flux in Turbulent Disks
480
954 Stationary Magnetospheres on Kerr Black Holes
486
955 Relaxation of Black Hole Magnetospheres and the BlandfordZnajek Process
499
96 Magnetic SpinDown of Rotating Black Holes
509
Problems
511
Physics of Accretion Flows around Compact Objects
513
101 Angular Momentum Transport
514
102 Magnetohydrodynamics for Accretion Disks
517
1022 Time and Space Discretization
523
1023 MRI Driven Turbulence in Disks
525
1024 TwoTemperature Plasmas and Radiation Pressure in Accretion Disks
533
103 States of Turbulent Accretion Disks
537
1031 Turbulent Angular Momentum Transport in Accretion Disks
538
1032 Truncated Accretion and Standard Disk Models in 1D
540
1033 Standard Thin Disk Solutions SSD
545
1034 AdvectionDominated Flows ADAF
551
1035 SuperEddington Accretion
552
1036 Unified Models of Disk Accretion
553
1037 Fundamental TimeScales for Accreting Black Holes
555
104 Relativistic MHD Turbulent Accretion onto Black Holes
558
1042 The Equations for GRMHD
559
1043 Nonradiative Accretion onto Rotating Black Holes
563
105 Jets and the Ergosphere
565
1051 Jets as Outflows from the Ergospheric Region
566
1052 From the Ergosphere to the Cluster Gas
572
Problems
575
Epilogue and Future Prospects
578
Astrophysical Constants and Symbols
587
SLy4 Equation of State for Neutron Star Matter
591
3+1 Split of Spacetime Curvature
595
C2 CodazziMainardi Equations
596
3+1 Split of Rotating Neutron Star Geometry
598
D2 The Curvature of Time Slices
601
Equations of GRMHD
605
E2 Conservative Formulation of GRMHD
607
E3 Numerical Schemes
609
Solutions
613
Glossary
640
References
657
Index
675
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