Gravitation, Part 3This landmark text offers a rigorous fullyear graduate level course on gravitation physics, teaching students to: • Grasp the laws of physics in flat spacetime • Predict orders of magnitude • Calculate using the principal tools of modern geometry • Predict all levels of precision • Understand Einstein's geometric framework for physics • Explore applications, including pulsars and neutron stars, cosmology, the Schwarzschild geometry and gravitational collapse, and gravitational waves • Probe experimental tests of Einstein's theory • Tackle advanced topics such as superspace and quantum geometrodynamics The book offers a unique, alternating twotrack pathway through the subject: • In many chapters, material focusing on basic physical ideas is designated as Track 1. These sections together make an appropriate oneterm advanced/graduate level course (mathematical prerequisites: vector analysis and simple partialdifferential equations). The book is printed to make it easy for readers to identify these sections. • The remaining Track 2 material provides a wealth of advanced topics instructors can draw from to flesh out a twoterm course, with Track 1 sections serving as prerequisites. 
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Review: Gravitation
User Review  GR Reader  GoodreadsI read this when I was twelve and made my own models of tensors out of egg boxes. My mother says she still has them up in the loft. Read full review
Review: Gravitation
User Review  Ron Banister  GoodreadsStill working through the Tensor Calculus!! LOL Read full review
Contents
SPACETIME PHYSICS  1 
5  9 
PHYSICS IN FLAT SPACETIME  45 
Farewell to ict  51 
Differentials  63 
The Electromagnetic Field  71 
Lorentz force law defines fields predicts  72 
Tensors in All Generality  74 
Mass and Angular Momentum of Fully Relativistic Sources  451 
Mass and Angular Momentum of a Closed Universe  457 
Conservation Laws for 4Momentum and Angular Momentum  460 
Gaussian Flux Integrals for 4Momentum and Angular Momentum  461 
Volume Integrals for 4Momentum and Angular Momentum  464 
Why the Energy of the Gravitational Field Cannot be Localized  466 
Conservation Laws for Total 4Momentum and Angular Momentum  468 
Equation of Motion Derived from the Field Equation  471 
ThreePlusOne View Versus Geometric View  78 
Maxwells Equations  79 
Working with Tensors  81 
Electromagnetism and Differential Forms  90 
Differential forms and exterior calculus  91 
Electromagnetic 2Form and Lorentz Force  99 
From honeycomb to abstract 2form  102 
Forms Illuminate Electromagnetism and Electromagnetism Illuminates Forms  105 
Duality of 2forms  108 
Radiation Fields 1 10  111 
Maxwells Equations  112 
Exterior Derivative and Closed Forms 1 14  114 
Progression of forms and exterior deriva  115 
Distant Action from Local Law  120 
1 5  126 
StressEnergy Tensor and Conservation Laws 1 30  130 
Threedimensional volumes  135 
Components of StressEnergy Tensor  137 
StressEnergy Tensor for a Swarm of Particles  138 
StressEnergy Tensor for a Perfect Fluid  139 
Electromagnetic StressEnergy  140 
Symmetry of the StressEnergy Tensor  141 
Integral Formulation  142 
Differential Formulation  146 
Volume integrals surface integrals and Gausss  147 
Sample Application of V T 0  152 
Newtonian hydrodynamics reviewed 1 53  153 
Angular Momentum  156 
Accelerated Observers  163 
Hyperbolic Motion  166 
Constraints on Size of an Accelerated Frame  168 
The Tetrad Carried by a Uniformly Accelerated Observer  169 
The Tetrad FermiWalker Transported by an Observer with Arbitrary Acceleration  170 
The Local Coordinate System of an Accelerated Observer 1 72  172 
Incompatibility of Gravity and Special Relativity  177 
Gravitational Redshift Derived from Energy Conservation  187 
Gravitational Redshift as Evidence for the Principle of Equivalence  189 
Local Flatness Global Curvature  190 
THE MATHEMATICS OF CURVED SPACETIME  193 
An Overview 1 95  195 
Difference in Outlook and Power  197 
Pictorial Abstract Component  198 
Tensor Algebra in Curved Spacetime  201 
Parallel Transport Covariant Derivative Connection Coefficients Geodesies  207 
Mathematical Discussion  217 
Geodesic Deviation and the Riemann Curvature Tensor  218 
Differential Topology  225 
Vector and Directional Derivative Refined into Tangent Vector  226 
Bases Components and Transformation Laws for Vectors  230 
1Forms  231 
Tensors  233 
Commutators and Pictorial Techniques  235 
Manifolds and Differential Topology  240 
Geodesies Parallel Transport and Covariant Derivative  244 
Pictorial Approach  245 
Abstract Approach  247 
terms of Schilds ladder  248 
Component Approach  258 
Geodesic Equation  262 
Geodesic Deviation and Spacetime Curvature  265 
Tidal Gravitational Forces and Riemann Curvature Tensor  270 
Parallel Transport Around a Closed Curve  277 
Flatness is Equivalent to Zero Riemann Curvature  283 
Riemann Normal Coordinates  285 
Newtonian Gravity in the Language of Curved Spacetime  289 
Stratification of Newtonian Spacetime  291 
Galilean Coordinate Systems  292 
Geometric CoordinateFree Formulation of Newtonian Gravity  298 
A Critique  302 
Metric as Foundation of All  304 
Metric  305 
Concord Between Geodesies of Curved Spacetime Geometry and Straight Lines of Local Lorentz Geometry  312 
Geodesies as World Lines of Extremal Proper Time  315 
MetricInduced Properties of Riemann  324 
The Proper Reference Frame of an Accelerated Observer  327 
Calculation of Curvature  333 
Forming the Einstein Tensor  343 
More Efficient Computation  344 
Curvature 2Forms  348 
Computation of Curvature Using Exterior Differential Forms  354 
Bianchi Identities and the Boundary of a Boundary  364 
Bianchi Identity ftf 0 as a Manifestation of Boundary of Boundary 0  372 
Key to Contracted Bianchi Identity  373 
Calculation of the Moment of Rotation  375 
Conservation of Moment of Rotation Seen from Boundary of a Boundary is Zero  377 
Conservation of Moment of Rotation Expressed in Differential Form  378 
A Preview  379 
EINSTEINS GEOMETRIC THEORY OF GRAVITY  383 
Equivalence Principle and Measurement of the Gravitational Field  385 
FactorOrdering Problems in the Equivalence Principle  388 
The Rods and Clocks Used to Measure Space and Time Intervals  393 
lines  397 
The Measurement of the Gravitational Field  399 
Automatic Conservation of the Source as the Central Idea in the Formulation of the Field Equation  404 
A Dynamic Necessity  408 
Cosmological Constant  409 
The Newtonian Limit  412 
Axiomatize Einsteins Theory?  416 
A Feature Distinguishing Einsteins Theory from Other Theories of Gravity  429 
A Taste of the History of Einsteins Equation  431 
Weak Gravitational Fields 1 I The Linearized Theory of Gravity  435 
Gravitational Waves  442 
Nearly Newtonian Gravitational Fields  445 
Mass and Angular Momentum of a Gravitating System  448 
Measurement of the Mass and Angular Momentum  450 
Variational Principle and InitialValue Data  484 
The Hilbert Action Principle and the Palatini Method of Variation  491 
Matter Lagrangian and StressEnergy Tensor  504 
Splitting Spacetime into Space and Time  505 
Intrinsic and Extrinsic Curvature  509 
The Hilbert Action Principle and the ArnowittDeserMisner Modification Thereof in the SpaceplusTime Split  519 
The ArnowittDeserMisner Formulation of the Dynamics of Geometry  520 
Integrating Forward in Time  526 
The InitialValue Problem in the ThinSandwich Formulation  528 
The TimeSymmetric and TimeAntisymmetric InitialValue Problem  535 
Yorks Handles to Specify a 4Geometry  539 
Machs Principle and the Origin of Inertia  543 
Junction Conditions  551 
4  565 
RELATIVISTIC STARS  591 
Pulsars and Neutron Stars Quasars and Supermassive Stars  618 
The Pit in the Potential as the Central New Feature of Motion  636 
try  674 
Stellar Pulsations  688 
THE UNIVERSE  701 
Evolution of the Universe into Its Present State  763 
Present State and Future Evolution of the Universe  771 
Anisotropic and Inhomogeneous Cosmologies  800 
GRAVITATIONAL COLLAPSE AND BLACK HOLES  817 
Gravitational Collapse  842 
Black Holes  872 
The Gravitational and Electromagnetic Fields of a Black Hole  875 
Mass Angular Momentum Charge and Magnetic Moment  891 
Symmetries and Frame Dragging  892 
Equations of Motion for Test Particles  897 
Principal Null Congruences  901 
Storage and Removal of Energy from Black Holes  904 
Reversible and Irreversible Transformations  907 
Global Techniques Horizons and Singularity Theorems  916 
Infinity in Asymptotically Flat Spacetime  917 
Causality and Horizons  922 
Global Structure of Horizons  924 
Proof of Second Law of BlackHole Dynamics  931 
Singularity Theorems and the Issue of the Final State  934 
GRAVITATIONAL WAVES  941 
Propagation of Gravitational Waves  943 
Review of Linearized Theory in Vacuum  944 
PlaneWave Solutions in Linearized Theory  945 
The Transverse Traceless TT Gauge  946 
Geodesic Deviation in a Linearized Gravitational Wave  950 
Polarization of a Plane Wave  952 
The StressEnergy Carried by a Gravitational Wave  955 
Gravitational Waves in the Full Theory of General Relativity  956 
An Exact PlaneWave Solution  957 
Physical Properties of the Exact Plane Wave  960 
Comparison of an Exact Electromagnetic Plane Wave with the Gravitational Plane Wave  961 
A New Viewpoint on the Exact Plane Wave  962 
The Shortwave Approximation  964 
Effect of Background Curvature on Wave Propagation  967 
StressEnergy Tensor for Gravitational Waves  969 
Generation of Gravitational Waves  974 
Power Radiated in Terms of Internal Power Flow  978 
Laboratory Generators of Gravitational Waves  979 
General Discussion  980 
Gravitational Collapse Black Holes Supernovae and Pulsars as Sources  981 
Binary Stars as Sources  986 
Formulas for Radiation from Nearly Newtonian SlowMotion Sources  989 
Radiation Reaction in SlowMotion Sources  993 
Foundations for Derivation of Radiation Formulas  995 
Evaluation of the Radiation Field in the SlowMotion Approximation  996 
Derivation of the RadiationReaction Potential  1001 
Detection of Gravitational Waves  1004 
Accelerations in Mechanical Detectors  1006 
Types of Mechanical Detectors  1012 
EXPERIMENTAL TESTS OF GENERAL RELATIVITY  1045 
Other Theories of Gravity and the PostNewtonian Approximation  1066 
SolarSystem Experiments  1096 
FRONTIERS  1133 
Lorentz Transformation via Spinor Algebra 1 142  1142 
Thomas Precession via Spinor Algebra 1 145  1145 
Spmors  1148 
Correspondence Between Vectors and Spinors 1 150  1150 
Spinor Algebra  1151 
Spin Space and Its Basis Spinors 1 1 56  1156 
Spinor Viewed as Flagpole Plus Flag Plus OrientationEntanglement  1157 
1 57  1158 
An Application of Spinors 1 160  1160 
Spinors as a Powerful Tool in Gravitation Theory 1 1 64  1164 
Regge Calculus 1 166  1166 
Simplexes and Deficit Angles  1167 
Skeleton Form of Field Equations  1169 
The Choice of Lattice Structure 1 173  1173 
tries out of lowerdimensional ones 1 1 76  1176 
Past Applications of Regge Calculus 1 1 78  1178 
The Future of Regge Calculus 1 1 79  1179 
Arena for the Dynamics of Geometry 1 180  1180 
The Dynamics of Geometry Described in the Language of the Superspace of the I3s  1184 
The EinsteinHamiltonJacobi Equation  1185 
Fluctuations in Geometry 1 1 90  1190 
Beyond the End of Time  1196 
Assessment of the Theory that Predicts Collapse 1 198  1198 
Their Prevalence and Final Dominance  1202 
Not Geometry but Pregeometry as the Magic Building Material 1 203  1203 
Pregeometry as the Calculus of Propositions  1208 
The Reprocessing of the Universe  1209 
1221  
1255  
1265  
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Common terms and phrases
3geometry 4momentum 4velocity acceleration angular momentum arbitrary basis vectors black hole calculation Chapter collapse components connection coefficients conservation constant coordinate system cosmological covariant derivative curvature tensor curved spacetime defined density diagram differential distance dynamic Einstein field equation electromagnetic field energy equation of motion equivalent event Exercise expansion exterior derivative Figure flat spacetime fluid function galaxies gauge geodesic deviation geometrodynamics given gravitational field gravitational waves horizon hypersurface initialvalue integral line element linearized theory Lorentz frame manifold massenergy mathematical matter measured Newtonian notation null observer orbit orthonormal parallel transport photon physics potential propagation proper quantities radiation radius redshift region relativistic rest frame rest mass result rotation scalar Schwarzschild coordinates Schwarzschild geometry Show singularity slice solution space spacelike spacelike hypersurface spherical star stressenergy tensor surface symmetry tangent vector test particles theorem timelike transformation universe vanish vector field velocity world line zero