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[资源] Compact Stars Nuclear Physics, Particle Physics and General Relativity

Contents
Preface  vii
1  Introduction  1
2
4
5
1.1  Compact  Stars  . . . . . . . . . . . . . . .
1.2  Compact  Stars  and  Relativistic Physics .
1.3  Compact  Stars  and  Dense-Matter  Physics
2  General  Relativity
2.1  Lorentz Invariance  ......  .
2.1.1  Lorentz  transformations
7
8
8
2.1.2  Covariant  vectors.  . . .  10
2.1.3  Energy-momentum  tensor  of  a perfect fluid  12
2.1.4  Light  cone.  . . . . . . . . . . . . . . . . . .  12
2.2  Scalars, Vectors,  and  Tensors in Curvilinear  Coordinates  13
2.3  Principle of Equivalence  of  Inertia  and  Gravitation  18
2.3.1  Photon  in a  gravitational  field  20
2.3.2  Tidal  gravity . . . . . . . . . . . .  21
2.3.3  Curvature  of  spacetime  ......  21
2.3.4  Energy  conservation  and  curvature  22
2.4  Gravity  ..  . . . . . . . . . . . . . . . . .  23
2.4.1  Mathematical  definition of local Lorentz frames  26
2.4.2  Geodesics..............  26
2.4.3  Comparison  with  Newton's gravity  29
2.5  Covariance  ................  30
2.5.1  Principle of General  Covariance.  .  30
2.5.2  Covariant Differentiation  .....  30
2.5.3  Geodesic  equation  from covariance  principle.  31
2.5.4  Covariant divergence  and  conserved  quantities  33
2.6  Riemann  Curvature  Tensor . . . . . . . . . . . . . . .  36
2.6.1  Second covariant derivative of scalars  and  vectors.  36
2.6.2  Symmetries  of  the  Riemann  tensor . .  36
2.6.3  Test for  flatness.  . . . . . . . . . . . .  37
2.6.4  Second covariant derivative of tensors  37
x  Contents
2.6.5  Bianchi  identities.
2.6.6  Einstein tensor  ..
2.7 Einstein's Field Equations
2.8 Relativistic Stars . . . . .
2.8.1  Metric in static isotropic  spacetime.
2.8.2  The  Schwarzschild solution  ...  . .
2.8.3  Riemann tensor outside a Schwarzschild  star
2.8.4  Energy-Momentum tensor of  matter  ..  .
2.8.5  The  Oppenheimer-Volkoff equations  ..  .
2.8.6  Gravitational collapse  and  limiting mass .
2.9  Action Principle in Gravity  ...........  .
3  Compact  Stars:
38
39
40
42
42
44
45
46
47
51
52
From  Dwarfs  to  Black  Holes  55
3.1  Birth  and  Death  of  Stars.  . . . . . . . . . .  55
3.2 Objective . . . . . . . . . . . . . . . . . . .  61
3.3 Gravitational Units  and  Neutron  Star  Size.  62
3.4  Partial  Decoupling of  Matter  from  Gravity.  66
3.5 Equations of Relativistic Stellar Structure  67
3.6 Electrical Neutrality of Stars  ......  71
3.7  "Constancy" of  the  Chemical  Potential.  .  72
3.8 Gravitational Redshift . . . . . . . . . . .  73
3.8.1  Integrity of  an  atom  in strong fields  73
3.8.2  Redshift in a general  static  field  ..  75
3.8.3  Comparison of  emitted  and  received light  78
3.8.4  Measurements of  M / R  from redshift  79
3.9 White Dwarfs  and  Neutron Stars . . . . . . . . .  79
3.9.1  Overview . . . . . . . . . . . . . . . . . .  79
3.9.2  Fermi-Gas equation of  state  for nucleons  and  electrons  81
3.9.3  High- and  low-density  limits.  . . . . . .  86
3.9.4  Poly tropes  and  Newtonian white dwarfs  87
3.9.5  Stability..................  91
3.9.6  Nonrelativistic electron  region.  . . . . .  93
3.9.7  Relativistic electron region: asymptotic white dwarf
mass.  . . . . . . . . . . . . . . . . . . . . . . . .  ..  94
3.9.8  Nature  of  limiting mass of dwarfs  and  neutron  stars  96
3.9.9  Degenerate ideal gas  neutron  star.  .  98
3.10 Improvements in  White  Dwarf Models . . .  99
3.10.1  Nature  of  matter  at  dwarf densities.  99
3.10.2  Carbon  and  oxygen white dwarfs . .  102
3.11 Stellar Sequences from  White  Dwarfs  to  Neutron  Stars.  105
3.12  Star  of Uniform Density . . . . . . . . . . .  107
3.13 Baryon Number of a  Star  . . . . . . . . . .  110
3.14 Bound on Maximum Mass of Neutron Stars  112
3.15 Beyond Maximum-Mass Neutron  Stars.  . .  116
Contents  xi
3.16  Black  Holes.  . . . . . . . . . . . . .  117
3.16.1  Interior  and  Exterior Regions  117
3.16.2  No statics within . .  120
3.16.3  Black hole densities  ....  122
4  Relativistic  Nuclear  Field  Theory  124
4.1  Motivation  .............  124
4.2  Lagrange Formalism . . . . . . . .  129
4.3  Symmetries  and  Conservation  Laws.  130
4.3.1  Internal global  symmetries.  131
4.3.2  Spacetime symmetries . . . .  132
4.4  Boson and Fermion Fields .  ...  . . .  135
4.4.1  Uncharged  and  charged scalar fields  135
4.4.2  Uncharged  and  charged vector fields  136
4.4.3  Dirac fields . . . . . .  138
4.4.4  Neutron  and  proton  .  140
4.4.5  Electromagnetic field .  142
4.5  Properties of Nuclear  Matter  143
4.6  The  (j  - w  Model.  . . . . . .  147
4.7  Stationarity of Energy Density  156
4.8  Model  with  Scalar Self-Interactions.  156
4.8.1  Algebraic determination of  the  coupling constants  158
4.8.2  Symmetric nuclear  matter  equation of  state  161
4.8.3  Negative self-interaction .  162
4.9  Introduction of Isospin Force  ..  164
4.10  Inclusion of  the  Octet  of Baryons  169
4.11  High-Density  Limit.  . . . . . . .  173
4.12  Effective vs. Renormalized Theory  173
4.13  Bound vs. Unbound Neutron  Matter  175
4.13.1  Bound  neutron  matter  . . . .  176
4.13.2  First-Order phase  transition.  176
4.14  Note on Dimensions  178
4.15  Summary . . . . . . . . . . . . . . .  178
5  Neutron  Stars  180
5.1  Introduction......................  180
5.2  Pulsars:  The  Observational Basis of Neutron Stars  183
5.2.1  Important  pulsar discoveries. . . . .  183
5.2.2  Pulsar  periods  ............  186
5.2.3  Individual pulses  and  pulse profiles .  187
5.2.4  Detection biases  ...........  189
5.2.5  Two populations of pulsars . . . . .  190
5.2.6  Supernova associations with pulsars  191
5.2.7  Why  pulsars are neutron  stars  193
5.2.8  Pulsar  masses . . . . . . . . . . . . .  197
xii  Contents
5.2.9  Pulsar ages . . . . . . . . . . . .  200
5.2.10 Evolution of  the  braking index 5  .  202
5.3 Theory of Neutron  Stars.  . . . . . . . .  206
5.3.1  Nuclear  and  neutron  star  matter:  Similarities  and  dif-
ferences . . . . . . . . . . . . . . . . .  206
5.3.2  Chemical equilibrium in a  star  . . . .  208
5.3.3  Hadronic composition of  neutron  stars  212
5.3.4  Neutron  star  matter  . . . . . . . . . .  214
5.3.5  Hints for computation . . . . . . . . .  219
5.3.6  Isospin- and  charge-favored baryon species.  221
5.3.7  Surface of neutron  stars  . . . . . . . . .  221
5.3.8  Reprise of white dwarfs  to  neutron  stars  222
5.3.9  Development of  neutron  star  sequences.  223
5.3.10 Mass as a function of central  density.  .  224
5.3.11 Radius-Mass characteristic relationship  225
5.4 Constitution of Neutron  Stars.  . . . . . . . . .  227
5.4.1  Limiting mass  and  the  equation of  state  227
5.4.2  Beta  equilibrium  and  symmetry energy  228
5.4.3  Hyperon  stars.  . . . . . . . . . . . . . .  229
5.4.4  Limiting mass  and  hyperon populations  233
5.4.5  Compression modulus  and  effective nucleon mass  234
5.4.6  Pion  and  kaon condensation . . . . . . . . .  236
5.4.7  Charge neutrality achieved among baryons  240
5.5 Tables of Equations of  State.  242
5.5.1  Low  density.  242
5.5.2  High density  244
6  Rotating  Neutron  Stars  247
6.1  Motivation  ...................  247
6.2 Dragging of Local Inertial  Frames.  . . . . . .  249
6.3 Interior Solution for  the  Dragging Frequency  253
6.4 Kepler Angular Velocity in General Relativity .  255
6.5  Effect of Frame Dragging  on  Kepler Frequency  258
6.6  Hartle-Thorne Perturbative  Solution.  . . . . .  260
6.6.1  Comparison  of  Perturbative  and  Numerical Solutions  261
6.7 Imprint of Angular Momentum . . . . . . . . . .  262
6.8  Rotating Stars  with  Realistic Equations of  State  263
6.9  Effect of Rotation on Stellar  Structure  264
6.10 Gravitational-Wave  Instabilities.  . . . . . . . .  265
7  Limiting  Rotational  Period  of  Neutron  Stars  275
7.1  Motivation  ........  275
7.2  The  Minimal Constraints  ............  277
7.3  Variational Ansatz . . . . . . . . . . . . . . . .  278
7.4  Limiting Value of Rotational Period as a Function of  Mass.  279
7.5
7.6
7.7
7.8
Test of Sensitivity  of  Results  .....
General Relativistic Limit on  Rotation
Discussion  and  Alternatives
Summary
Contents  xiii
281
285
286
288
8  Quark  Stars  289
289
289
290
291
292
293
295
301
8.1  Introduction  ...........  .
8.2  Quark  Matter  Equation  of  State
8.2.1  Zero  Temperature  ....
8.2.2  Massless  quark  approximation
8.2.3  First  order  in  O:s  •
8.3  Quark  Star  Matter  . . . . . . . . . . .
8.4  Strange  and  Charm  Stars  . . . . . . .
8.5  Beyond  White  Dwarfs  and  Neutron  Stars
9  Hybrid  Stars
9.1  Introduction.
303
303
9.2  Constant-Pressure  Phase  Transition  .............  305
9.3  The  Confined-Deconfined  Phase  Transition  in  Neutron  Stars  308
9.3.1  Conservation laws are  global-not  local . . .  308
9.4  Degrees of Freedom  in  a Multicomponent  System.  .  309
9.4.1  Coulomb  lattice  structure  of  the  mixed phase  313
9.4.2  Phase  diagram  . . . . . .  313
9.4.3  Two energy scales  ...............  314
9.5  Gross  Structure  of a  Hybrid  Star  . . . . . . . . . . .  315
9.5.1  Energy  budget  in  the  reapportionment  of charge  317
9.6  Crystalline  Structure  . . . . . . . . . . . . . . . . . . . .  319
9.6.1  Crystalline  structure  as a function of stellar  mass.  323
9.6.2  Possible implications for glitches . . . . . . .  325
9.7 Mechanism for  Formation  of Low-Mass Black  Holes.  326
9.7.1  Hyperonization-Induced collapse  328
9.7.2  Deconfinement-Induced  collapse.  329
9.7.3  Density profiles . . . . . . . . . .  330
9.7.4  Discussion.............  331
9.8  Tables of  Equation  of  State  for  Hybrid  Stars.  333
10  Strange  Stars  337
10.1  The  Strange  Matter  Hypothesis.  . . . . . . . . . . . .  ..  337
10.2 Compatibility of  the  Hypothesis  with  Present  Knowledge  338
10.2.1 Energetic considerations . . . . . . . . . . . . .  ..  338
10.2.2  The  universe  and  its  evolution  ...........  339
10.2.3 Stability  of  nuclei against decay  to  strange  matter  340
10.2.4 Stability  of  nuclei  to  conversion  by  strange  nuggets  341
10.2.5 Terrestrial  searches.  . . . . . . . . .  341
10.2.6 Summary, prospects  and  challenges.  . . . . . .  ..  343
xiv  Contents
10.3 Sub millisecond  Pulsars  . . . . . . . . . .  343
10.3.1  The  fine-tuning  problem.  . . . .  343
10.3.2  Limits  to  neutron  star  rotation.  344
10.3.3 Implausibly high  central  densities  345
10.3.4 Strange  stars  as fast rotors . . . .  346
10.3.5  Out  of  the  impasse.  . . . . . . . .  347
10.3.6 Motivation for searches  and  prospects for  discovery.  348
10.4  Structure  of Strange  Stars  . . . . . . . .  348
10.5  Strange  Stars  to  Strange  Dwarfs  .....  350
10.5.1  Strange  stars  with  nuclear crusts .  350
10.5.2  Strange  dwarfs  with  nuclear  crusts  355
10.5.3 Stability . . . . . . . . . . . . . . .  357
10.5.4 Possible new class of dense white dwarfs  360
10.6 Conclusion  ..............  .  361
Appendix  A:  Useful  Astronomical  Data  362
Books  for  Further  Study  363
References  365
Index  383

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