Special and General Relativity: With Applications to White Dwarfs, Neutron Stars and Black Holes / Edition 1

Special and General Relativity: With Applications to White Dwarfs, Neutron Stars and Black Holes / Edition 1

by Norman K. Glendenning
     
 

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ISBN-10: 0387471065

ISBN-13: 9780387471068

Pub. Date: 03/28/2007

Publisher: Springer New York

Special and General Relativity are concisely developed together with essential aspects of nuclear and particle physics. Problem sets are provided for many chapters, making the book ideal for a course on the physics of white dwarf and neutron star interiors.

About the Author:
Norman K. Glendenning is Senior Scientist Emeritus at the Nuclear Science

Overview

Special and General Relativity are concisely developed together with essential aspects of nuclear and particle physics. Problem sets are provided for many chapters, making the book ideal for a course on the physics of white dwarf and neutron star interiors.

About the Author:
Norman K. Glendenning is Senior Scientist Emeritus at the Nuclear Science Division, Institute for Nuclear and Particle Astrophysics, Lawrence Berkeley National Laboratory at the University of California, Berkeley

Product Details

ISBN-13:
9780387471068
Publisher:
Springer New York
Publication date:
03/28/2007
Series:
Astronomy and Astrophysics Library Series
Edition description:
2007
Pages:
228
Product dimensions:
6.30(w) x 9.30(h) x 0.60(d)

Table of Contents


Preface     vii
Introduction     1
Compact Stars     2
Compact Stars and Relativistic Physics     5
Compact Stars and Dense-Matter Physics     6
Special Relativity     9
Lorentz Invariance     11
Lorentz transformations     11
Time Dilation     14
Covariant vectors     14
Energy and Momentum     16
Energy-momentum tensor of a perfect fluid     17
Light cone     18
General Relativity     19
Scalars, Vectors, and Tensors in Curvilinear Coordinates     20
Photon in a gravitational field     28
Tidal gravity     29
Curvature of spacetime     30
Energy conservation and curvature     30
Gravity     32
Einstein's Discovery     32
Particle Motion in an Arbitrary Gravitational Field     32
Mathematical definition of local Lorentz frames     35
Geodesics     36
Comparison with Newton's gravity     38
Covariance     39
Principle of general covariance     39
Covariant differentiation     40
Geodesic equation from covarianceprinciple     41
Covariant divergence and conserved quantities     42
Riemann Curvature Tensor     45
Second covariant derivative of scalars and vectors     45
Symmetries of the Riemann tensor     46
Test for flatness     47
Second covariant derivative of tensors     47
Bianchi identities     48
Einstein tensor     48
Einstein's Field Equations     50
Relativistic Stars     52
Metric in static isotropic spacetime     53
The Schwarzschild solution     54
Riemann tensor outside a Schwarzschild star     55
Energy-Momentum tensor of matter     56
The Oppenheimer-Volkoff equations     57
Gravitational collapse and limiting mass     62
Action Principle in Gravity     63
Derivations     65
Problems for Chapter 3     68
Compact Stars: From Dwarfs to Black Holes     70
Birth and Death of Stars     70
Aim of this Chapter     78
Gravitational Units and Neutron Star Size     79
Units     79
Size and number of baryons in a star     82
Gravitational energy of a neutron star      84
Partial Decoupling of Matter from Gravity     85
Equations of Relativistic Stellar Structure     87
Interpretation     87
Boundary conditions and stellar sequences     90
Electrical Neutrality of Stars     92
"Constancy" of the Chemical Potential     93
Gravitational Redshift     95
Integrity of an atom in strong fields     95
Redshift in a general static field     96
Comparison of emitted and received light     100
Measurements of M/R from redshift     100
White Dwarfs and Neutron Stars     101
Overview     101
Fermi-Gas equation of state for nucleons and electrons     103
High and low-density limits     109
Polytropes and Newtonian white dwarfs     112
Nonrelativistic electron region     116
Ultrarelativistic electron region: asymptotic white dwarf mass     116
Nature of limiting mass of dwarfs and neutron stars     120
Degenerate ideal gas neutron star     121
Improvements in White Dwarf Models     123
Nature of matter at dwarf and neutron star densities     123
Low-density equation of state     126
Carbon and oxygen white dwarfs      127
Temperature and Neutron Star Surface     130
Stellar Sequences from White Dwarfs to Neutron Stars     133
Density Distribution in Neutron Stars     136
Baryon Number of a Star     137
Binding Energy of a Neutron Star     138
Star of Uniform Density     140
Scaling Solution of the OV Equations     142
Bound on Maximum Mass of Neutron Stars     144
Stability     148
Necessary condition for stability     149
Normal modes of vibration: Sufficient condition for stability     151
Beyond the Maximum-Mass Neutron Star     152
Hyperons and Quarks in Neutron Stars     155
First Order Phase Transitions in Stars     156
Degrees of freedom and driving forces     157
Isospin symmetry energy as a driving force     159
Geometrical phases     162
Color-flavor locked quark-matter phase (CFL)     162
Signal of Quark Deconfinement in Neutron Stars     165
Neutron Star Twins     171
Particle populations in twins     173
Test for stability     174
Formation and detection     175
Black Holes     176
Interior and exterior regions      176
No statics within     179
Black hole densities     182
Black Hole Evaporation     182
Kerr Metric for Rotating Black Hole     183
Problems for Chapter 4     184
Cosmology     187
Foreword     187
Units and Data     188
World Lines and Weyl's Hypothesis     188
Metric for a uniform isotropic universe     189
Friedmann-Lemaitre Equations     190
Temperature Variation with Expansion     192
Expansion in the Three Ages     192
Redshift     194
Hubble constant and Universe age     194
Evolution of the Early Universe     195
Temperature and Density of the Early Universe     196
Derivation of the Planck Scale     197
Time-scale of Neutrino Interactions     198
Neutrino Reaction Time-scale Becomes Longer than the Age of the Universe     198
Ionization of Hydrogen     199
Present Photon and Baryon Densities     199
Expansion Since Equality of Radiation and Mass     200
Helium Abundance     201
Helium Abundance is Primeval     201
Redshift and Scale Factor Relationship      201
Collapse Time of a Dust Cloud     202
Jeans Mass     203
Jeans Mass in the Radiation Era     203
Jeans Mass in the Matter Era     204
Early Matter Dominated Universe     205
Curvature     206
Acceleration     207
References     209
Index     217

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