Gravitation in Astrophysics: Cargèse 1986

Gravitation in Astrophysics: Cargèse 1986

Paperback(Softcover reprint of the original 1st ed. 1987)

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Gravitation in Astrophysics: Cargèse 1986 by B. Carter

With the discovery of pulsars, quasars, and galactic X-ray sources in the late 60's and early 70's, and the coincident expansion in the search for gravitational waves, rela­ tivistic gravity assumed an important place in the astrophysics of localized objects. Only by pushing Einstein's solar-system-tested general theory of relativity to the study of the extremes of gravitational collapse and its outcomes did it seem that one could explain these frontier astronomical phenomena. This conclusion continues to be true today. Relativistic gravity had always played the central role in cosmology. The discov­ ery of the cosmic background radiation in 1965, the increasing understanding of matter physics at high energies in the decades following, and the growing wealth of observations on the large scale structure meant that it was possible to make increasingly detailed mod­ els of the universe, both today and far in the past. This development, not accidentally, was contemporary to that for localized objects described above.

Product Details

ISBN-13: 9781461290568
Publisher: Springer US
Publication date: 10/19/2011
Series: Nato Science Series B: , #156
Edition description: Softcover reprint of the original 1st ed. 1987
Pages: 399
Product dimensions: 6.10(w) x 9.25(h) x 0.03(d)

Table of Contents

I. Gravitation in Localized Systems.- An Introduction to the Theory of Gravitational Radiation.- 1. Introduction.- 1.1 Scope of these lectures.- 1.2 Conventions and Notation.- 2. What is a Gravitational Wave?.- 2.1 First viewpoint: propagation of discontinuities.- 2.2 Second viewpoint: high-frequency waves.- 2.3 Third viewpoint: weak gravitational waves on a flat background.- 2.4 Other viewpoints.- 3. Basic Problems of Gravitational Radiation Theory.- 3.1 A catalogue of problems.- 3.2 A catalogue of approximation methods.- 4. Quadrupole Moment Formalisms.- 4.1 “Quadrupole laws” versus “quadrupole equations”.- 4.2 The three “quadrupole laws”.- 4.3 General discussion of “quadrupole equations”.- 4.4 The “standard,” or “Einstein,” far-field quadrupole equation.- 4.5 The “Landau-Lifshitz” quadrupole equation.- 4.6 The “Fock” quadrupole equation.- 4.7 Recent improvements.- 4.8 Thorne’s generation formalism.- 4.9 Tentative conclusion about the “standard” far-field quadrupole equation.- 4.10 Far-field quadrupole equations for some specific problems.- 4.11 The generalized quadrupole equation of Halpern-Desbrandes and Press.- 4.12 The far-field multipole law.- 4.13 On the definition of the asymptotic outgoing radiation field.- 4.14 Energy-loss quadrupole equations.- 4.15 Radiation-reaction quadrupole equations à la Burke-Thorne.- 4.16 Post-Newtonian radiation-reaction quadrupole equations.- 4.17 Radiation-reaction quadrupole equations in the N-body problem.- 4.18 Conclusion.- 5. Multipolar-Post-Minkowskian Formalisms.- 5.1 Introduction.- 5.2 Formal framework.- 5.3 The hierarchy of equations to be solved.- 5.4 The first step of the hierarchy.- 5.5 On the meaning of the “algorithmic multipole moments”.- 5.6 Recursive algorithm for constructing the higher steps of the hierarchy.- 5.7 Partial results on the asymptotic problem.- 5.8 Preliminary results on the propagation problem.- 5.9 Partial results on the generation problem.- 5.10 Preliminary results on the radiation-reaction problem.- 6. Gravitational Radiation and Binary Systems of Condensed Objects.- 6.1 One method for two questions.- 6.2 The two-condensed-body problem in General Relativity.- 6.3 The internal problems.- 6.4 The matching: internal ? external.- 6.5 The external problem.- 6.6 A convenient auxiliary mathematical technique.- 6.7 Answer to the first question of §6.1 (generation).- 6.8 Equations of motion of a binary system of condensed bodies.- 6.9 Radiation-reaction force versus the relativistic Laplace effect.- 6.10 Poincaré on gravitational waves.- 6.11 Answer to the second question of §6.1 (radiation reaction).- 6.12 Application to the binary pulsar PSR 1913+.- 6.13 Conclusion.- Acknowledgements.- Some Books Fully Devoted to Gravitational Radiation.- Bibliographical References.- Mathematical Foundations of the Theory of Relativistic Stellar and Black Hole Configurations.- 1. Introduction.- 1.1 Background.- 1.2 Purpose and Plan.- 2. Notions of General (Dynamic) Black Hole Theory.- 2.1 Definition.- 2.2 Kinematics of Characteristic (Null) Boundaries.- 2.3 Generalised Raychaudhuri Equation for Timelike and Null Geodesic Congruences.- 2.4 The Horizon of a Black Hole.- 2.5 Asymptotic Predictability, Closed Trapped Surfaces, and Apparent Horizons.- 2.6 Cosmic Censorship and the Existence of an Asymptotic Equilibrium.- 2.7 Approximate Equilibrium.- 3. Stationary and Static Equilibrium.- 3.1 Overview.- 3.2 Elementary Local Properties of Killing Horizons.- 3.3 Uniformity of the Corotating Potential on a Killing Horizon.- 3.4 Uniformity of K (the “zeroth law”) on a Killing Horizon.- 3.5 The Mass of a Stationary System.- 3.6 Globally Bradyonic Character of Generators of Stationary D.O.C..- 3.7 The Staticity Theorem for Non-Rotating Electromagnetic Black Holes.- 3.8 Local Characterisation of Simply Connected Static Domain of Outer Communications.- 4. Axisymmetric Equilibrium States.- 4.1 Mass and Angular Momentum of Stationary Axisymmetric Systems.- 4.2 Circularity Theorem for Stationary Axisymmetric Systems.- 4.3 The Ergoregion and ZAMOs in Papapetrou Coordinates.- 4.4 Slowly Rotating (but Strongly Gravitating) Stellar Equilibrium Configurations.- 4.5 Killing Horizon (Nullity and Rigidity) Property of Locus Where ZAMOs Go Null.- 4.6 Black Hole Mass and Angular Momentum and their Variations.- 4.7 Superradiance.- 4.8 Local Characterisation of Simply Connected Stationary (Circularity) Axisymmetric D.O.C..- 5. The Source Free Equilibrium State Problem for Axisymmetric Black Holes.- 5.1 Canonical Global Coordinate System for the D.O.C. of a Stationary Axisymmetric Black Hole.- 5.2 Reduction to a 2-dimensional Boundary Problem.- 5.3 The Final Step in the Uniqueness Theorem.- 5.4 Killing-Maxwell-Yano System.- 5.5 The Canonical Tetrad.- Acknowledgements.- References.- Relativistic Gravitational Instabilities.- Spherical Pulsation of Spherical Stars.- Newtonian stars.- Relativistic stars.- The turning point criterion for white dwarfs and neutron stars.- Star clusters.- Nonspherical Pulsation of Spherical Stars.- Newtonian stars.- Relativistic stars.- Strongly damped modes.- Quadrupole gravitational radiation.- Nonspherical Perturbations of Spherical Black Holes.- Formulation as a scattering problem.- Calculations of the normal modes.- Stability of Rotating Stars: General Remarks.- The Maclaurin Spheroids.- The nonaxisymmetric modes.- The secular instabilities.- The T/W criterion for instability.- A Relativistic Approach to Stability.- Perfect fluids in general relativity.- Definition of a perturbation in terms of a sequence of solutions.- Two preferred perturbations; Eulerian and Lagrangian.- Perturbations of Einstein’s Equations.- A stability criterion.- A Simple Approach to the Radiation Instability.- Conserved quantities for wave fields.- Mechanism for the gravitational wave instability.- Gravitational wave instability as a two-stream instability.- Other ways of exciting the instability.- The instability due to viscosity.- The Perturbed Energy of a Rotating System.- Orbiting particle: an elementary example.- The second-order energy of a rotating fluid.- Maximum Rotation Rate of Neutron Stars.- Stability of the Kerr Black Hole.- References.- Accretion and Collapse.- I. The Gravothermal Catastrophe.- 1. Specific Heats.- 2. A Thought Experiment.- 3. Why Self-Similar Solutions Occur in Science.- 4. Evolution After Core Collapse.- II. Spherical Accretion.- 5. Bondi Accretion.- 6. Relativistic Accretion.- 7. Cold Self-Similar Gravitational Collapse.- III. Disk Accretion.- 8. Energy, Angular Momentum and Dissipation.- 9. Viscous Newtonian Accretion Disks.- 10. Relativistic Accretion Disks.- IV. Optically Thick Accretion.- 11. Self-Similar Solutions.- 12. Enthalpy Theorem and Jet Production.- Accretion Disk Electrodynamics.- 1. The Standard Thin Disk.- 2. Turbulent Dynamo in Accretion Disks.- 3. Electrodynamic Coupling of Accretion-Disk Coronae.- 4. The Interaction of a Neutron Star with an Accretion Disk.- 4.1 Spin up of neutron stars.- 4.2 Quasiperiodic oscillations.- References.- Special Topics I.- The Membrane Paradigm for Black-Hole Astrophysics.- Tidal Disruption.- 1. Introduction.- 2. Tidal Tensor.- 3. Ellipsoidal Deformations of Homogeneous Bodies.- 3.1 The stationary rotational problem.- 3.2 The stationary tidal problem.- 3.3 The dynamical tidal problem.- 4. Tidal Deformations of a Compressible Body.- 4.1 The tidal rolling mill effect.- 4.2 Tidal versus collisional disruption of stars.- 4.3 The affine star model.- 4.4 Motion in relativistic tidal field.- 4.5 Pancake nucleosynthesis and the fate of debris.- References.- Naked Singularities in Spherical Gravitational Collapse.- 1. Introduction.- 2. Dust Collapse and Shell Focusing Singularities.- 2.1 Shell-crossing.- 2.2 Tolman-Bondi solutions.- 2.3 Causal structure of the Tolman-Bondi solutions.- 2.4 Interpretation of shell-focusing singularities.- 2.5 Collapse of null fluid.- 3. Collapse of Scalar Field Configurations.- 3.1 Self-similar collapse.- 3.2 Generic spherical collapse.- Acknowledgements.- References.- II. Gravitation in Cosmology.- Some Topics in Relativistic Cosmology.- Orientation.- The Universe is Unique.- Non-local Influences.- Horizons.- How Many Spatial Dimensions are There?.- Variation of Fundamental “Constants”.- Unknown Physics.- Selection Effects.- Unknown Matter Fields.- How Little Could We Know?.- Newtonian Gravitation.- Newtonian Cosmology.- General Relativistic Cosmology.- The Friedman Cosmological Models.- Observable Parameters.- When Do Closed Universes Recollapse?.- Spatially Homogeneous Universes.- The Microwave Background and the Density of the Universe.- Microwave Background Observations.- Characteristic Microwave Background Patterns.- Quadrupole.- Hotspot.- Spirals.- Observational Limits.- Isotropy and Homogeneity.- The Cosmological Principle(s).- Can We Prove a Cosmological Principle?.- Is Isotropy a Stable Property of Cosmological Models?.- Is Isotropy Really Unstable and Does it Matter Anyway?.- Approach to a Family of Plane Waves.- No Hair Theorems.- Inflation and the Initial Value Problem.- Inflation and the Strong Energy Condition.- The Deflationary Universe.- Resumé.- Acknowledgements.- References.- Cosmic Strings and the Origin of Structure in the Universe.- 1. Introduction.- 1.1 Origin of Perturbations in the Universe.- 2. Quantum Particle Creation in an Inflationary Universe.- 2.1 A Simple Model.- 2.2 More Realistic Models.- 3. Topological Defects in Field Theories.- 3.1 Cosmological Constant.- 3.2 Domain Walls.- 3.3 Cosmic Strings.- 3.4 Monopoles.- 3.5 Instantons.- 4. Cosmological Evolution of Topological Defects.- 4.1 Bounds on Evolution of Defect Density.- 4.2 Evolution of Monopoles and Domain Walls.- 4.3 Evolution of Cosmic Strings.- 5. Motion and Evolution of Cosmic Strings.- 5.1 Closed Loops.- 5.2 Gravitational Waves from Closed Loops.- 5.3 Galaxy Formation by Cosmic Strings.- 5.4 Fluctuations in the Cosmic Background Radiation Due to Cosmic Strings.- 5.5 Light Bending Due to Cosmic Strings.- Acknowledgements.- References.- Cosmological Phase Transitions.- 1. The Evolution of the Vacuum.- 1.1 High Temperature Symmetry Restoration.- 1.2 Domain Walls.- 1.3 Cosmic Strings.- 1.4 Magnetic Monopoles.- 1.5 The Kibble Mechanism.- 2. Inflation.- 2.1 Loose Ends of the Standard Cosmology.- 2.2 Inflation - The Basic Picture.- 2.3 Dynamics of Inflation.- 2.4 Specific Models.- 2.5 Present Status and Future Directions.- Acknowledgements.- References.- Prediction in Quantum Cosmology.- 1. Introduction.- 2. Predictions from the Wave Function of the Universe.- 2.1 The Wave Function of the Universe.- 2.2 Cosmological Observations and Cosmological Predictions.- 2.3 The Nature of Cosmological Predictions.- 2.4 Quantum Mechanics of Individual Systems.- 2.5 The Problem of Time.- 3. Laws for Initial Conditions.- 3.1 The Sum Over Histories Formulation of Quantum Cosmology.- 3.2 Constraints.- 3.3 A Proposal for a Wave Function of the Universe.- 4. The Limit of Classical Geometry and Quantum Field Theory in Curved Spacetime.- 4.1 The Semiclassical Approximation to Non-Relativistic Particle Quantum Mechanics.- 4.2 The Born-Oppenheimer Approximation for Real Clocks.- 4.3 The Approximation of Quantum Field Theory in Curved Spacetime.- 4.4 The Semiclassical Vacuum.- Acknowledgements.- Problems.- References.- Special Topics II.- The Quasi-Isotropic Universe.- 1. Introduction.- 2. The Microwave Background.- 3. Helium Abundance.- 4. Anisotropic Spatially Homogeneous Cosmologies.- 5. The Wainwright and Anderson Solution.- 6. An Inhomogeneous Model.- 7. Discussion of Results.- 7.1 The Anthropic Principle.- 7.2 Initial Conditions.- 7.3 Gravitational Entropy.- References.- Semiclassical Quantum Gravity in Two and Four Dimensions.- 1. Quantum Effects Near Distorted Black Holes.- 2. Q.F.T and the Antipodal Identification of Black Holes and of Desitter Space.- 3. The Back-Reaction Problem in Two Dimensions: Liouville and Schroedinger Equations.- References.- Towards a Theory for the Quantum Mechanics of Gravitational Collapse.- Abstract.- 1. Introduction.- 2. String Theory in a Nut Shell.- 3. The Black Hole.- 4. The Shifting Horizon.- 5. A Link with String Theory.- 6. Conclusion.- References.

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