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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
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Add Compact Objects in Astrophysics: White Dwarfs, Neutron Stars and Black Holes, Modern comprehensive introduction and overview of the physics of White Dwarfs, Neutron Stars and Black Holes, including all relevant observations. Contains a basic introduction to General Relativity, including the modern 3+1 split of spacetime and of E, Compact Objects in Astrophysics: White Dwarfs, Neutron Stars and Black Holes to the inventory that you are selling on WonderClubX
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Add Compact Objects in Astrophysics: White Dwarfs, Neutron Stars and Black Holes, Modern comprehensive introduction and overview of the physics of White Dwarfs, Neutron Stars and Black Holes, including all relevant observations. Contains a basic introduction to General Relativity, including the modern 3+1 split of spacetime and of E, Compact Objects in Astrophysics: White Dwarfs, Neutron Stars and Black Holes to your collection on WonderClub |