Black Hole Gravitohydromagnetics (eBook)

Preface 6
Contents 8
Introduction 14
1.1 Introductory Physical Perspective 14
1.2 Evidence for Astrophysical Black Holes 15
1.3 Extragalactic Radio Sources 19
1.3.1 Unified Scheme for Radio Loud AGN 21
1.3.2 Quantifying the Power of Extragalactic Radio Sources 28
1.3.3 Summary of Evidence of a Black Hole Central Engine in Radio Loud AGN 36
1.4 Extracting Energy from a Black Hole 38
1.5 Historical Perspective 44
1.6 Black Hole GHM 45
Relativistic Plasma Physics 47
2.1 Introduction 47
2.2 The Equations of Perfect MHD Plasmas 48
2.3 Perfect MHDWave Speeds in aWarm Plasma 50
2.4 Covariant Formulation of the PlasmaWave Speeds 56
2.5 The Perfect MHD Alfv • en Mode 57
2.6 The Magneto-Acoustic Waves in a Perfect MHD Plasma 59
2.7 MHD Waves in a Resistive Medium 60
2.8 High FrequencyWaves in a Perfect MHD Plasma 62
2.9 The Cylindrical Plasma-FilledWaveguide 63
2.9.1 Plasma Waves in a Cylindrical Waveguide 63
2.9.2 Fast Waves 65
2.9.3 Alfv • en Waves 66
2.9.4 The Faraday Wheel 67
2.10 Anisotropic Electrical Conductivity in Strong Magnetic Fields 77
2.11 High FrequencyWaves in Protonic Plasmas 82
2.12 Longitudinal Polarized MHD Discontinuities 84
2.13 What is Important About This Chapter? 86
2.14 Appendix. The Role of the Alfv • enWave in the Plasma-Filled Waveguide 87
2.14.1 Constructing Wave Packets 87
2.14.2 Physical Discussion 90
Particle Trajectories in the Ergosphere 91
3.1 Motivation 91
3.2 Coordinate Systems and Frames 91
3.3 Geodesic Motion 94
3.4 The Momentum Equations of a Magneto-Fluid 96
3.5 Frame Dragging and Negative Energy States 102
3.6 MaxwellÌs Equations 104
3.7 Inviscid Hydromagnetic Horizon Boundary Conditions 106
3.7.1 Electromagnetic Forces 108
3.7.2 Radiative Forces 113
3.7.3 Other Possible Forces in the Equation of Motion 113
Vacuum Electrodynamics 115
4.1 Motivation 115
4.2 Maxwell’s Equations in the Newman–Penrose Formalism 116
4.3 PoissonÌs Equations in the Kerr SpaceÒTime 124
4.4 LaplaceÌs Equations in the Kerr SpaceÒTime 126
4.5 The Electrodynamics of the Event Horizon 130
4.5.1 Electromagnetic Sources of PoissonÌs Equations Near the Horizon 130
4.5.2 External Fields From Electromagnetic Sources Near the Horizon 134
4.6 Simple Solutions to LaplaceÌs Equations 140
4.7 The Horizon Electromagnetic Boundary Conditionont 146
4.8 The Charge of a Rotating Black Hole 158
4.9 The Example of Axisymmetric Current Loops 160
4.9.1 Magnetic Flux Exclusion From Rapid Rotators 160
4.9.2 The No Hair Theorem 160
4.9.3 Magnetic Field Line Reconnection Near the Event Horizon 162
4.9.4 The Physical Interpretation of the Results 163
4.10 The Implications of Vacuum Electrodynamics to GHM 164
Magnetically Dominated Time Stationary Perfect MHDWinds 165
5.1 The Perfect MHD Wind Equations 166
5.2 Constants of Motion within a Flux Tube 167
5.3 TheWind Equations 170
5.4 The Critical Surfaces 171
5.5 The Topology of the Outgoing MHD Wind Solution Space 175
5.6 The Minimum Torque Solution 177
5.7 The GradÒShafranov Equation 179
Perfect MHDWinds andWaves in the Ergosphere 184
6.1 Paired MHD Winds 185
6.2 Ingoing Perfect MHD ErgosphericWinds 188
6.3 The Horizon is an Asymptotic Infinity to MHD Winds 189
6.4 Outgoing FastWaves Near the Horizon 193
6.4.1 The Vacuum Electrodyanmic Equations 194
6.4.2 Current Sources Near the Horizon 196
6.4.3 Solutions of the Inhomogeneous MaxwellÌs Equations Near the Horizon 198
6.4.4 Outgoing Fast Waves Near the Fast Point 198
6.4.5 The Singular Set of Long Wavelength Solutions 200
6.4.6 The Linearized Perturbation Equations for Short Wavelength Modes 204
6.4.7 Outgoing Magnetic Stresses Carried Fast Waves Near the Horizon 212
6.4.8 The Singular Point Structure of the Wave Equation Near the Fast Critical Surface 213
6.4.9 Comparison to the Locally Covariant Calculation of Chapter 2 216
6.4.10 Summary of Results 218
6.5 Causality and the BlandfordÒZnajek Horizon Boundary Condition 219
Ergosphere Driven Winds 223
7.1 Analogy to the Physics of the Faraday Wheel 223
7.2 Causal Determination of the Constants of Motion 224
7.2.1 Axisymmetric Vacuum Electromagnetic Fields 224
7.2.2 The Gravitational Field 225
7.2.3 Light Waves and Waves in a Highly Dissipative Medium 225
7.2.4 Perfect MHD Waves and Mildly Dissipative MHD Waves 226
7.3 The Causal Structure of the Dynamo 227
7.3.1 Radial Gravity 228
7.3.2 The Dragging of Inertial Frames 228
7.4 The Torsional Tug of War 229
Ergospheric Disk Dynamos 233
8.1 Fate of Accreted Magnetic Flux 233
8.2 The Global Structure of the Flow 240
8.2.1 Poynting Flux and Disk Formation 240
8.2.2 The Slow Shock and Disk Atmosphere 241
8.2.3 Some General Disk Structure 243
8.3 The RankineÒHugoniot Relations 243
8.3.1 The Field Line Angular Velocity 244
8.3.2 The Specific Enthalpy of the Post Shock Gas 245
8.3.3 The Density of the Post Shock Gas 247
8.3.4 The Downstream Poloidal Velocity 248
8.4 A Parametric Realization of Shock Parameters 249
8.5 The Dynamics and Structure of the Disk 249
8.6 The Global Energetics of the Disk 253
8.7 Near the Stationary Limit 255
8.8 The Inner Edge of the Disk 255
8.9 Summary 256
Winds From Event Horizon Magnetospheres 258
9.1 Time Dependent Dissipative Winds 258
9.2 The Causal Determination of O 261
9.3 The Ergospheric Dynamo in Free Floating Flux Tubes 265
9.4 Perfect MHD Paired Outgoing Minimum TorqueWinds: 270
9.4.1 Mathematical Formulation of Paired Wind as a Boundary Value Problem 271
9.4.2 The Outgoing Minimum Torque Wind 272
9.4.3 Initial Data for the Ingoing Wind 273
9.4.4 The Force Free Limit of the Ingoing Wind 274
9.4.5 The Poloidal Equation of Motion of the Ingoing Wind 277
9.4.6 Numerically Quantifying the Wind Near the Inner Light Cylinder 279
9.4.7 Accessibility of the Inner Alfv • en Point 281
9.4.8 Accessibility of the Inner Fast Point 284
9.4.9 The Terminus of the Perfect MHD Wind 290
9.4.10 The Ingoing Extension of the Subcritical Solution 292
9.5 The Radiative Instability Near the Light Cylinder 293
9.5.1 The Initial Unperturbed State 295
9.5.2 The Radiation Resistance Perturbation 295
9.5.3 The Perturbed Four Velocity 296
9.5.4 The Perturbed Field Strengths 297
9.5.5 The Perturbed Proper Electric Field 299
9.5.6 Stationary Point Analysis 301
9.6 The Dynamo Region 304
9.6.1 Resistivity and the Saturation of the Instability 304
9.6.2 The Anchor Point 306
9.6.3 Causal Structure of the Dynamo 309
9.6.4 The Global Energetics of the Dynamo 310
9.7 The Deflagration Wind 313
9.7.1 The Near Zone 313
9.7.2 The Breakdown of Near Zone Physics 315
9.7.3 The Asymptotic Wind Zone 317
9.8 The Unique Physical Solution 318
Applications to the Theory of Extragalactic Radio Sources 320
10.1 Spectral Diagnostics of Blazar Central Engines 320
10.1.1 BL Lacs and Quasars 324
10.1.2 Other Correlations 325
10.2 The Black Hole GHM Theory of the Central Engine 327
10.2.1 The Distribution of Poloidal Magnetic Flux 329
10.2.2 The Structure of the Ergospheric Disk 333
10.3 The Electromagnetic Power From the Three Component Central Engine 334
10.4 Applications of the Theory 339
10.4.1 Interpreting the Unified Scheme 339
10.4.2 Correlations with Blazar Spectra 347
10.4.3 Radio Source Evolution 349
10.5 The GHM Theory of Extragalactic Radio Sources 352
Numerical Results 355
11.1 The Current State of Numerical Simulations 356
11.2 Simulations of Relativistic Strings 361
11.3 Ergospheric Disk Jets in 3-D MHD Accretion Flow Simulations 367
11.3.1 The Equatorial Poynting Flux Source in KDJ 369
11.3.2 The Vertical Flux in the Equatorial Dynamo 371
11.3.3 The Field Line Angular Velocity 373
11.3.4 The Creation of Negative Energy Plasma 374
11.3.5 The Simulation KDE 377
11.4 Source of Poynting Flux in Event Horizon Magnetospheres 379
11.4.1 The Propagation of the Ergospheric Disk Jet 382
11.4.2 The MHD Coronal Piston 384
11.5 Discussion 390
11.5.1 The Ergospheric Disk Jet 390
11.5.2 The Truncated Ergospheric Disk Jet 390
11.5.3 The BlandfordÒZnajek Jet 391
11.5.4 The KDJ Ergospheric Disk Data Point 391
11.5.5 The KDE Ergospheric Disk Data Point 392
11.5.6 The KDH Ergospheric Disk Data Point 392
11.5.7 Constraints Imposed by Observations 393
References 395
Index 400