COMPACT STARS
CONTENTS COMPACT OBJECTS IN ASTROPHYSICS WHY IS NEWTONIAN GRAVITY OBSOLETE? EINSTEIN WAS SKEPTICAL ABOUT THE EXISTENCE OF BLACK HOLES SUBRAHMANYAN CHANDRASEKHAR AND COMPACT OBJECTS CLASSES OF COMPACT OBJECTS WHITE DWARFS AND NEUTRON STARS COMPACT X-RAY SOURCES RADIO PULSARS SUPERMASSIVE BLACK HOLES IN GALACTIC CENTERS GAMMA-RAY BURSTERS PROBLEMS GRAVITY OF COMPACT OBJECTS GEOMETRIC CONCEPTS AND GENERAL RELATIVITY THE BASIC PRINCIPLES OF GENERAL RELATIVITY EINSTEIN’S EQUIVALENCE PRINCIPLE AND METRICITY METRIC THEORIES OF GRAVITY BASIC CALCULUS ON MANIFOLDS TENSORS AND FORMS ON MANIFOLDS THE METRIC FIELD AND PSEUDO-RIEMANNIAN MANIFOLDS THE CALCULUS OF FORMS ON LORENTZIAN MANIFOLDS AF?NE CONNECTION AND COVARIANT DERIVATIVE AF?NE CONNECTION COVARIANT DERIVATIVE OF VECTOR FIELDS COVARIANT DERIVATIVE FOR TENSOR FIELDS PARALLEL TRANSPORT AND METRIC CONNECTION METRIC CONNECTION DIVERGENCE OF VECTOR FIELDS CURVATURE OF PSEUDO-RIEMANNIAN MANIFOLDS MATHEMATICAL DE?NITION OF TORSION AND CURVATURE BIANCHI IDENTITIES FOR METRIC CONNECTION RICCI, WEYL AND EINSTEIN TENSOR CARTAN’S STRUCTURE EQUATIONS GRAVITY IS A LORENTZIAN CONNECTION ON SPACETIME THE FOUR KEY PRINCIPLES OF GENERAL RELATIVITY THE HILBERT ACTION AND EINSTEIN’S FIELD EQUATIONS ON THE COSMOLOGICAL CONSTANT LIMITS OF GENERAL RELATIVITY GRAVITATIONAL WAVES THE GEODESIC DEVIATION – RELATIVISTIC TIDAL FORCES GRAVITY WAVE EXPERIMENTS THE NATURE OF GRAVITATIONAL WAVES DEGREES OF FREEDOM GRAVITATIONAL WAVE SOLUTIONS THE QUADRUPOLE FORMULA 3+1 SPLIT OF EINSTEIN’S EQUATIONS INDUCED SPATIAL METRIC AND EXTRINSIC CURVATURE HYPERSURFACE EMBEDDING SPLIT OF AF?NE CONNECTION AND CURVATURE SPLIT OF EINSTEIN’S EQUATIONS BLACK HOLE SIMULATIONS AND GRAVITATIONAL WAVES MATTER MODELS FOR COMPACT OBJECTS GENERAL RELATIVISTIC HYDRODYNAMICS RELATIVISTIC PLASMA EQUATIONS ON NUMERICS OF HYDRODYNAMICS THE BOLTZMANN EQUATION IN GR THE GEODESICS SPRAY ON THE COTANGENT BUNDLE PARTICLE NUMBER CURRENT AND ENERGY–MOMENTUM TENSOR THE RELATIVISTIC BOLTZMANN EQUATION LIOUVILLE OPERATOR IN 3+1 SPLIT TRANSFORMATION INTO THE LOCAL REST FRAME RELATIVISTIC STELLAR STRUCTURE SPACETIME OF RELATIVISTIC STARS DERIVATION OF THE TOV EQUATIONS THE CURVATURE OF STATIC SPACETIMES MATTER IN THE INTERIOR THE EXTERIOR SCHWARZSCHILD SOLUTION STABLE BRANCHES FOR DEGENERATE STARS METRIC FOR RELATIVISTIC STARS A VARIATIONAL PRINCIPLE FOR THE STELLAR STRUCTURE WHITE DWARFS OBSERVATIONS OF ISOLATED WHITE DWARFS SIRIUS B FIELD WHITE DWARFS AND CLASSI?CATION WHITE DWARFS IN GLOBULAR CLUSTERS MAGNETIC WHITE DWARFS ULTRACOOL WHITE DWARFS AS COSMOCHRONOMETERS WHAT IS INSIDE A WHITE DWARF? EQUATION OF STATE BELOW THE NEUTRON DRIP DENSITY STRUCTURE OF WHITE DWARFS AND THE CHANDRASEKHAR MASS POLYTROPIC APPROXIMATION BEYOND THE CHANDRASEKHAR TREATMENT COMPARISON WITH OBSERVATIONS THE RELATIVISTIC INSTABILITY OF WHITE DWARF STARS NECESSARY CONDITION FOR STABILITY THE TOTAL ENERGY IN THE POST-NEWTONIAN LIMIT GR WHITE DWARF INSTABILITY COOLING WHITE DWARFS STRUCTURE OF THE SURFACE LAYERS COOLING CURVES AND CRYSTALLIZATION TESTING WD CRYSTALLIZATION THEORY WHITE DWARFS IN BINARY SYSTEMS NEUTRON STARS THE STRUCTURE OF A NEUTRON STAR EQUATIONS OF STATE BEYOND NEUTRON DRIP FROM NEUTRON DRIP TO SATURATION NUCLEAR EOS FOR DENSE NEUTRON MATTER RELATIVISTIC MEAN FIELD THEORY ABOVE SATURATION ANALYTICAL FITS TO EOS NEUTRON STAR MODELS HADRONIC MODELS QUARK MATTER CORES GRAND CANONICAL POTENTIAL FOR QUARK MATTER STRANGE QUARK STARS THE STRUCTURE OF MASSIVE NEUTRON STARS NEUTRON STARS IN CLOSE BINARY SYSTEMS POST-NEWTONIAN POTENTIALS FOR MANY-BODY SYSTEMS PERIASTRON SHIFT IN TWO-BODY SYSTEMS THE SHAPIRO TIME DELAY IN A BINARY SYSTEM DECAY OF BINARY ORBITS DUE TO GRAVITATIONAL RADIATION MASSES OF NEUTRON STARS FROM RADIO PULSAR TIMING WHAT IS PULSAR TIMING? THE TIMING FORMULA TIMING OF THE BINARY SYSTEM PSR B1913+16 MASSES OF COMPANION STARS THE DOUBLE PULSAR SYSTEM PSR 0737-3039A+B NEUTRON STARS IN OUR GALAXY 100 MILLION NEUTRON STARS IN THE GALAXY THERMAL EMISSION FROM ISOLATED NEUTRON STARS ROTATION-POWERED PULSARS ACCRETION-POWERED NEUTRON STARS AND THE MASS–RADIUS RELATION RAPIDLY ROTATING NEUTRON STARS SPACETIME OF STATIONARY AND AXISYMMETRIC ROTATING BODIES PHYSICAL INTERPRETATION OF THE METRIC GEODETIC AND LENSE–THIRRING PRECESSION ON GENERAL 3+1 SPLIT OF SPACETIME EINSTEIN’S FIELD EQUATIONS FOR ROTATING OBJECTS RICCI TENSORS OF TIME-SLICES EXTRINSIC CURVATURE AND 4D RICCI TENSORS STELLAR STRUCTURE EQUATIONS IN ISOTROPIC GAUGE THE ISOTROPIC GAUGE STRUCTURE EQUATIONS FOR ROTATING STARS MECHANICAL EQUILIBRIUM AND EFFECTIVE POTENTIAL STELLAR PARAMETERS THE SLOW-ROTATION APPROXIMATION NUMERICAL INTEGRATION OF THE STELLAR STRUCTURE EQUATIONS COMPARISON OF NUMERICAL CODES PROPERTIES OF ROTATING EQUILIBRIUM STELLAR STRUCTURES TOWARDS ANALYTICAL VACUUM SOLUTIONS FOR ROTATING NEUTRON STARS WEYL–PAPAPETROU FORM ERNST EQUATIONS MANKO’S SOLUTION ON OSCILLATION AND FORMATION OF ROTATING NEUTRON STARS BLACK HOLES THE SCHWARZSCHILD BLACK HOLE TORTOISE COORDINATES AND NULL CONES ROADS TOWARDS BLACK HOLE FORMATION THE KRUSKAL EXTENSION PENROSE DIAGRAM – THE CONFORMAL STRUCTURE OF IN?NITY GEODETIC MOTIONS IN SCHWARZSCHILD SPACETIME A LAGRANGIAN THE EFFECTIVE POTENTIAL FOR EQUATORIAL MOTION ORBITAL EQUATION AND BOUND ORBITS IN SCHWARZSCHILD SPACETIME THE KERR BLACK HOLE KERR BLACK HOLE IN BOYER–LINDQUIST COORDINATES A SHORT DERIVATION OF THE KERR SOLUTION THE WEYL–PAPAPETROU FORM OF THE KERR METRIC UNIQUENESS OF THE KERR SOLUTION GLOBAL PROPERTIES OF THE KERR METRIC ON THE CONFORMAL STRUCTURE OF THE KERR SOLUTION ERNST’S EQUATIONS FOR THE KERR GEOMETRY THE KERR–SCHILD METRIC AND TWO-BLACK-HOLE STATES ROTATIONAL ENERGY AND THE FOUR LAWS OF BLACK HOLE EVOLUTION SURFACE GRAVITY AND ANGULAR VELOCITY OF THE HORIZON FIRST LAW OF BLACK HOLE DYNAMICS ROTATIONAL ENERGY OF ASTROPHYSICAL BLACK HOLES ON THE SECOND AND THIRD LAWS OF BLACK HOLE DYNAMICS TIME EVOLUTION OF BLACK HOLES QUASISTATIONARY EVOLUTION OF ACCRETING BLACK HOLES MERGING OF BLACK HOLES GEODESICS IN THE KERR GEOMETRY DIRECT INTEGRATION OF GEODESICS EQUATIONS GEODESICS IN THE EQUATORIAL PLANE GEODESICS INCLUDING LATERAL MOTION NULL GEODESICS AND RAY-TRACING IN KERR GEOMETRY DARK ENERGY STARS WHY DARK ENERGY STARS? STRUCTURE OF GRAVASTARS THE NECESSITY OF AN ANISOTROPIC CRUST ASTROPHYSICAL BLACK HOLES CLASSES OF ASTROPHYSICAL BLACK HOLES MEASURING BLACK HOLE MASSES BHS IN X-RAY BINARIES INTERMEDIATE-MASS BLACK HOLES SUPERMASSIVE BLACK HOLES IN NEARBY GALAXIES BLACK HOLES IN QUASARS ESTIMATING BLACK HOLE SPIN BLACK HOLE SPIN AND RADIO GALAXIES SPECTRAL FITTING OF ACCRETION DISKS RELATIVISTIC IRON LINES QUASIPERIODIC OSCILLATIONS BLACK HOLES AND GALAXY FORMATION BLACK HOLE MAGNETOSPHERES THE 3+1 FORMALISM FOR MAXWELL’S EQUATIONS PLASMA EQUATIONS IN THE 3+1 SPLIT TIME EVOLUTION OF MAGNETIC AND CURRENT FLUX IN TURBULENT DISKS STATIONARY MAGNETOSPHERES ON KERR BLACK HOLES RELAXATION OF BLACK HOLE MAGNETOSPHERES AND THE BLANDFORD–ZNAJEK PROCESS MAGNETIC SPIN-DOWN OF ROTATING BLACK HOLES PHYSICS OF ACCRETION FLOWS AROUND COMPACT OBJECTS 10 1 ANGULAR MOMENTUM TRANSPORT 10 2 MAGNETOHYDRODYNAMICS FOR ACCRETION DISKS 10 2 1 EQUATIONS OF MAGNETOHYDRODYNAMICS 10 2 2 TIME AND SPACE DISCRETIZATION 10 2 3 MRI DRIVEN TURBULENCE IN DISKS 10 2 4 TWO-TEMPERATURE PLASMAS AND RADIATION PRESSURE IN ACCRETION DISKS 10 3 STATES OF TURBULENT ACCRETION DISKS 10 3 1 TURBULENT ANGULAR MOMENTUM TRANSPORT IN ACCRETION DISKS 10 3 2 TRUNCATED ACCRETION AND STANDARD DISK MODELS IN 1D 10 3 3 STANDARD THIN DISK SOLUTIONS (SSD) 10 3 4 ADVECTION-DOMINATED FLOWS (ADAF) 10 3 5 SUPER-EDDINGTON ACCRETION 10 3 6 UNI?ED MODELS OF DISK ACCRETION 10 3 7 FUNDAMENTAL TIME-SCALES FOR ACCRETING BLACK HOLES 10 4 RELATIVISTIC MHD – TURBULENT ACCRETION ONTO BLACK HOLES 10 4 1 FROM SRMHD TO GRMHD 10 4 2 THE EQUATIONS FOR GRMHD 10 4 3 NONRADIATIVE ACCRETION ONTO ROTATING BLACK HOLES 10 5 JETS AND THE ERGOSPHERE 10 5 1 JETS AS OUT?OWS FROM THE ERGOSPHERIC REGION 10 5 2 FROM THE ERGOSPHERE TO THE CLUSTER GAS EPILOGUE AND FUTURE PROSPECTS ASTROPHYSICAL CONSTANTS AND SYMBOLS SLY4 EQUATION OF STATE FOR NEUTRON STAR MATTER 3+1 SPLIT OF SPACETIME CURVATURE GAUSS DECOMPOSITION CODAZZI–MAINARDI EQUATIONS 3+1 SPLIT OF ROTATING NEUTRON STAR GEOMETRY D 1 THE 3+1 SPLIT OF THE CONNECTION D 2 THE CURVATURE OF TIME SLICES EQUATIONS OF GRMHD ELECTROMAGNETIC FIELDS CONSERVATIVE FORMULATION OF GRMHD NUMERICAL SCHEMES SOLUTIONS