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

Compact Objects in Astrophysics     1
Why is Newtonian Gravity Obsolete?     1
Einstein was Skeptical about the Existence of Black Holes     3
Subrahmanyan Chandrasekhar and Compact Objects     4
Classes of Compact Objects     5
White Dwarfs and Neutron Stars     8
Compact X-Ray Sources     9
Radio Pulsars     11
Supermassive Black Holes in Galactic Centers     16
Gamma-Ray Bursters     19
Problems     25
Gravity of Compact Objects     27
Geometric Concepts and General Relativity     27
The Basic Principles of General Relativity     29
Einstein's Equivalence Principle and Metricity     29
Metric Theories of Gravity     33
Basic Calculus on Manifolds     37
Tensors and Forms on Manifolds     37
The Metric Field and Pseudo-Riemannian Manifolds     42
The Calculus of Forms on Lorentzian Manifolds     44
Affine Connection and Covariant Derivative     47
Affine Connection     47
Covariant Derivative of Vector Fields     47
Covariant Derivative for Tensor Fields     48
Parallel Transport and Metric Connection     50
Metric Connection     52
Divergence of Vector Fields     55
Curvature of Pseudo-Riemannian Manifolds     56
Mathematical Definition of Torsion and Curvature     57
Bianchi Identities for Metric Connection     58
Ricci, Weyl and Einstein Tensor     60
Cartan's Structure Equations     61
Gravity is a Lorentzian Connection on Spacetime     65
The Four Key Principles of General Relativity     65
The Hilbert Action and Einstein's Field Equations     68
On the Cosmological Constant     69
Limits of General Relativity     71
Gravitational Waves     73
The Geodesic Deviation - Relativistic Tidal Forces     73
Gravity Wave Experiments     74
The Nature of Gravitational Waves     76
Degrees of Freedom     79
Gravitational Wave Solutions     83
The Quadrupole Formula     87
3+1 Split of Einstein's Equations     91
Induced Spatial Metric and Extrinsic Curvature     92
Hypersurface Embedding     93
Split of Affine Connection and Curvature     95
Split of Einstein's Equations     98
Black Hole Simulations and Gravitational Waves      100
Problems     101
Matter Models for Compact Objects     105
General Relativistic Hydrodynamics     105
Relativistic Plasma Equations     106
On Numerics of Hydrodynamics     110
The Boltzmann Equation in GR     113
The Geodesics Spray on the Cotangent Bundle     113
Particle Number Current and Energy-Momentum Tensor     116
The Relativistic Boltzmann Equation     117
Liouville Operator in 3+1 Split     118
Transformation into the Local Rest Frame     119
Problems     120
Relativistic Stellar Structure     123
Spacetime of Relativistic Stars     123
Derivation of the TOV Equations     125
The Curvature of Static Spacetimes     125
Matter in the Interior     127
The Exterior Schwarzschild Solution     130
Stable Branches for Degenerate Stars     131
Metric for Relativistic Stars     131
A Variational Principle for the Stellar Structure     132
Problems     134
White Dwarfs     137
Observations of Isolated White Dwarfs     138
Sirius B     138
Field White Dwarfs and Classification      139
White Dwarfs in Globular Clusters     143
Magnetic White Dwarfs     143
Ultracool White Dwarfs as Cosmochronometers     145
What is Inside a White Dwarf?     151
Equation of State below the Neutron Drip Density     153
Structure of White Dwarfs and the Chandrasekhar Mass     159
Polytropic Approximation     160
Beyond the Chandrasekhar Treatment     162
Comparison with Observations     162
The Relativistic Instability of White Dwarf Stars     167
Necessary Condition for Stability     168
The Total Energy in the Post-Newtonian Limit     169
GR White Dwarf Instability     171
Cooling White Dwarfs     174
Structure of the Surface Layers     175
Cooling Curves and Crystallization     177
Testing WD Crystallization Theory     179
White Dwarfs in Binary Systems     180
Problems     185
Neutron Stars     187
The Structure of a Neutron Star     188
Equations of State beyond Neutron Drip     189
From Neutron Drip to Saturation     190
Nuclear EoS for Dense Neutron Matter     199
Relativistic Mean Field Theory above Saturation     206
Analytical Fits to EoS     216
Neutron Star Models     219
Hadronic Models     219
Quark Matter Cores     224
Grand Canonical Potential for Quark Matter     231
Strange Quark Stars     241
The Structure of Massive Neutron Stars     242
Neutron Stars in Close Binary Systems     244
Post-Newtonian Potentials for Many-Body Systems     244
Periastron Shift in Two-Body Systems     248
The Shapiro Time Delay in a Binary System     250
Decay of Binary Orbits due to Gravitational Radiation     251
Masses of Neutron Stars from Radio Pulsar Timing     255
What is Pulsar Timing?     255
The Timing Formula     259
Timing of the Binary System PSR B1913+16     263
Masses of Companion Stars     264
The Double Pulsar System PSR 0737-3039A+B     265
Neutron Stars in our Galaxy     269
100 Million Neutron Stars in the Galaxy     269
Thermal Emission from Isolated Neutron Stars     272
Rotation-Powered Pulsars     284
Accretion-Powered Neutron Stars and the Mass-Radius Relation     294
Problems     303
Rapidly Rotating Neutron Stars     307
Spacetime of Stationary and Axisymmetric Rotating Bodies     308
Physical Interpretation of the Metric     309
Geodetic and Lense-Thirring Precession     312
On General 3+1 Split of Spacetime     315
Einstein's Field Equations for Rotating Objects     317
Ricci Tensors of Time-Slices     318
Extrinsic Curvature and 4D Ricci Tensors     319
3+1 Split of Einstein's Equations     320
Stellar Structure Equations in Isotropic Gauge     321
The Isotropic Gauge     321
Structure Equations for Rotating Stars     322
Mechanical Equilibrium and Effective Potential     324
Stellar Parameters     326
The Slow-Rotation Approximation     332
Numerical Integration of the Stellar Structure Equations     335
Comparison of Numerical Codes     337
Properties of Rotating Equilibrium Stellar Structures     338
Towards Analytical Vacuum Solutions for Rotating Neutron Stars     342
Weyl-Papapetrou Form     342
Ernst Equations     343
Manko's Solution     345
On Oscillation and Formation of Rotating Neutron Stars     350
Problems      353
Black Holes     355
The Schwarzschild Black Hole     355
Tortoise Coordinates and Null Cones     356
Roads towards Black Hole Formation     358
The Kruskal Extension     359
Penrose Diagram - the Conformal Structure of Infinity     363
Geodetic Motions in Schwarzschild Spacetime     369
A Lagrangian     369
The Effective Potential for Equatorial Motion     371
Orbital Equation and Bound Orbits in Schwarzschild Spacetime     373
The Kerr Black Hole     378
Kerr Black Hole in Boyer-Lindquist Coordinates     379
A Short Derivation of the Kerr Solution     379
The Weyl-Papapetrou Form of the Kerr Metric     384
Uniqueness of the Kerr Solution     385
Global Properties of the Ken Metric     386
On the Conformal Structure of the Kerr Solution     393
Ernst's Equations for the Kerr Geometry     394
The Kerr-Schild Metric and Two-Black-Hole States     395
Rotational Energy and the Four Laws of Black Hole Evolution     399
Surface Gravity and Angular Velocity of the Horizon     400
First Law of Black Hole Dynamics     402
Rotational Energy of Astrophysical Black Holes      405
On the Second and Third Laws of Black Hole Dynamics     406
Time Evolution of Black Holes     408
Quasistationary Evolution of Accreting Black Holes     408
Merging of Black Holes     411
Geodesics in the Kerr Geometry     412
Direct Integration of Geodesics Equations     414
Geodesies in the Equatorial Plane     416
Geodesics Including Lateral Motion     424
Null Geodesics and Ray-Tracing in Kerr Geometry     431
Dark Energy Stars     442
Why Dark energy Stars?     442
Structure of Gravastars     443
The Necessity of an Anisotropic Crust     445
Problems     446
Astrophysical Black Holes     449
Classes of Astrophysical Black Holes     450
Measuring Black Hole Masses     451
BHs in X-Ray Binaries     451
Intermediate-Mass Black Holes     456
Supermassive Black Holes in Nearby Galaxies     456
Black Holes in Quasars     468
Estimating Black Hole Spin     470
Black Hole Spin and Radio Galaxies     471
Spectral Fitting of Accretion Disks     471
Relativistic Iron Lines     472
Quasiperiodic Oscillations     472
Black Holes and Galaxy Formation     472
Black Hole Magnetospheres     473
The 3+1 Formalism for Maxwell's Equations     474
Plasma Equations in the 3+1 Split     478
Time Evolution of Magnetic and Current Flux in Turbulent Disks     480
Stationary Magnetospheres on Kerr Black Holes     486
Relaxation of Black Hole Magnetospheres and the Blandford-Znajek Process     499
Magnetic Spin-Down of Rotating Black Holes     509
Problems     511
Physics of Accretion Flows around Compact Objects     513
Angular Momentum Transport     514
Magnetohydrodynamics for Accretion Disks     517
Equations of Magnetohydrodynamics     517
Time and Space Discretization     523
MRI Driven Turbulence in Disks     525
Two-Temperature Plasmas and Radiation Pressure in Accretion Disks     533
States of Turbulent Accretion Disks     537
Turbulent Angular Momentum Transport in Accretion Disks     538
Truncated Accretion and Standard Disk Models in ID     540
Standard Thin Disk Solutions (SSD)     545
Advection-Dominated Flows (ADAF)     551
Super-Eddington Accretion      552
Unified Models of Disk Accretion     553
Fundamental Time-Scales for Accreting Black Holes     555
Relativistic MHD - Turbulent Accretion onto Black Holes     558
From SRMHD to GRMHD     558
The Equations for GRMHD     559
Nonradiative Accretion onto Rotating Black Holes     563
Jets and the Ergosphere     565
Jets as Outflows from the Ergospheric Region     566
From the Ergosphere to the Cluster Gas     572
Problems     575
Epilogue and Future Prospects     579
Astrophysical Constants and Symbols     587
SLy4 Equation of State for Neutron Star Matter     591
3+1 Split of Spacetime Curvature     595
Gauss Decomposition     595
Codazzi-Mainardi Equations     596
3+1 Split of Rotating Neutron Star Geometry     599
The 3+1 Split of the Connection     599
The Curvature of Time Slices     601
Equations of GRMHD     605
Electromagnetic Fields     605
Conservative Formulation of GRMHD     607
Numerical Schemes     609
Solutions     613
Glossary     641
References     657
Index      675