General Relativity, Astrophysics, and Cosmology (Astronomy and Astrophysics Library)

Raychaudhuri, A.K.; Banerji, S.; Banerjee, A.

ISBN 10: 038740628X / ISBN 13: 9780387406282

Editore: Springer, 2003

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Codice articolo GG22408020009

Dati bibliografici

• Titolo: General Relativity, Astrophysics, and Cosmology (Astronomy and Astrophysics Library)
• Editore: Springer
• Data di pubblicazione: 2003
• Lingua: Inglese
• ISBN 10: 038740628X
• ISBN 13: 9780387406282
• Rilegatura: paperback
• Condizione: Fair
• Condizione della sovraccoperta: None as issued
• Peso: 16 once
• Cataloghi dei venditori:
  • Science:Astrophysics

Descrizione articolo

Riassunto

This book is intended for students interested in the applications of general relativity in astrophysics and cosmology but who would like to avoid mathematical complications. This volume thus combines relativity, astrophysics, and cosmology in a single volume. It provides an introduction to the subject that will enable students to consult more detailed treatises as well as the current literature. For prospective researchers in these fields, the book includes an appendix on differential forms, and an extensive, though not exhaustive list of references. The book is divided into three parts. The section on general relativity gives the case for a curved space-time, presents the mathematical background (tensor calculus, Riemannian geometry), discusses the Einstein equation and its solutions (including black holes, Penrose processes, and similar topics), and considers the energy-momentum tensor for various solutions. The section on relativistic astrophysics discusses stellar contraction and collapse, neutron stars and their equations of state, black holes, and accretion onto collapsed objects. The section on cosmology discusses various cosmological models, observational tests, and scenarios for the early universe.

Contenuti

I. The General Theory of Relativity.- 1. Introduction.- 1.1. The Case for Nonflat Space—Time.- 1.2. The Principle of Equivalence.- 1.3. Conflict Between the Equivalence Principle and the Pseudo-Euclidean Metric: Gravitational Redshift.- 1.4. A Fifth Force.- 2. Tensor Calculus and Riemannian Geometry.- 2.1. Riemannian Geometry and the Metric Tensor.- 2.2. Vectors and Tensors.- 2.3. Invariant Volume and Volume Integral.- 2.4. Affine Connection—Parallel Transport.- 2.5. Covariant Differentiation.- 2.6. The Differential Equation of a Geodesic.- 2.7. The Integrability of Parallel Displacement.- 2.8. The Riemann—Christoffel Tensor.- 2.9. The Bianchi Identity.- 2.10. The Ricci Tensor and the Einstein Tensor.- 2.11. The Weyl Tensor.- 2.12. Geodesic Deviation.- 3. Einstein’s Field Equations.- 3.1. Einstein’s Formulation of the Field Equations.- 3.2. Weak Field Approximation (Static Case).- 3.3. Gravitational Waves in Weak Field Approximation.- 3.4. Detection of Gravitational Waves.- 3.5. Integration of the Linearized Equations for a Stationary Axially Symmetric Distribution.- 3.6. The Action Principle and the Energy—Momentum Tensors.- 3.7. The Energy—Stress Tensor.- 3.8. The Einstein Equations from the Variational Principle.- 4. The Schwarzschild Metric and Crucial Tests.- 4.1. The Schwarzschild Solution.- 4.2. Birkhoff’s Theorem.- 4.3. Three Crucial Tests.- 4.4. The PPN Formalism.- 4.5. The Schwarzschild or the Spherically Symmetric Black Hole.- 4.6. Frequency Shift of Spectral Lines of Light Emitted by a Collapsing/Exploding Spherical Body.- 4.7. Fall in Apparent Luminosity of a Collapsing Body.- 4.8. Kruskal—Szekeres Coordinates.- 4.9. Historical Note on the Schwarzschild Black Hole.- 5. Electromagnetism in General Relativity.- 5.1. Introduction.- 5.2. The Field of a Charged Particle.- 5.3. Static Electrovac.- 5.4. The Already Unified Field Theory.- 6. Axially Symmetric Fields.- 6.1. The Lie Derivative and the Killing Equation.- 6.2. Static and Stationary Metrics.- 6.3. The Axially Symmetric Static Metric.- 6.4. Weyl’s Canonical Form.- 6.5. The Case of Two Mass Particles.- 6.6. The Schwarzschild Metric in the Form (6.21).- 6.7. Stationary Axisymmetric Vacuum Solutions.- 7. The Kerr Metric or the Rotating Black Hole.- 7.1. The Kerr Metric in Boyer—Lindquist Coordinates.- 7.2. The Black Hole Property.- 7.3. Locally Nonrotating Observers.- 7.4. The Horizon as a Null Surface.- 7.5. The Kerr—Newmann Metric.- 7.6. The Penrose Process.- 8. The Energy—Momentum Pseudotensor of the Gravitational Field and Loss of Energy by Gravitational Radiation.- 8.1. The Pseudo-Energy—Momentum Tensor.- 8.2. Historical Note.- 8.3. Loss of Energy by Gravitational Radiation.- 8.4. The Case of a Binary Star.- 9. Analysis of the Observational Data of the Hulse—Taylor Pulsar. Confirmation of the Einstein Quadrupole Radiation Formula.- II. Relativistic Astrophysics.- 10. White Dwarf Stars.- 10.1. Introduction.- 10.2. The Contraction of a Radiating Star in the Absence of Energy Generation.- 10.3. Degeneracy and the Equation of State.- 10.4. Limiting Mass for White Dwarfs.- 10.5. A Simple Argument for the Mass Limit.- 10.6. Critique of Chandrasekhar’s Result and Later Works.- 10.7. Historical Note.- 10.8. Observational Data on White Dwarfs.- 10.9. The Cooling and Age of White Dwarfs.- 11. Stellar Evolution, Supernovae, and Compact Objects.- 11.1. Introduction.- 11.2. The Evolution of Stars.- 11.3. The Dynamical Collapse.- 11.4. Some Numerical Results.- 11.5. Explosive Processes.- 11.6. Supernova 1987 A.- 12. Pulsars.- 12.1. Introduction.- 12.2. Distance from Dispersion Measure.- 12.3. Identification of Pulsars as Neutron Stars.- 12.4. The Energetics of Pulsar Emission.- 12.5. The Magnetic Field at the Pulsar Surface.- 12.6. The Age of Pulsars.- 12.7. Calculation of the Braking Index.- 12.8. The Nonvacuum Model.- 12.9. Observational Determination of Pulsar Masses.- 12.10. Cooling of Neutron Stars—Theory and Observation.- 12.11. The Influence of Superfluidity.- 12.12. The Influence of Pion Condensation.- 12.13. The Influence of Quarks.- 13. Spherically Symmetric Star Models.- 13.1. Introduction.- 13.2. The Tolman, Oppenheimer—Volkoff Equation.- 13.3. The Equation of State for Cold Catalyzed Matter.- 13.4. A Model of a Neutron Star and the Mass Limits.- 13.5. The Problems of the Upper Mass Limit of Neutron Stars.- 13.6. The Influence of Rotation, etc., on the Mass Limit.- 13.7. Note on the Stability of Compact Objects.- 14. Black Holes.- 14.1. Introduction.- 14.2. The No-Hair Theorem.- 14.3. The Laws of Black Hole Physics.- 14.4. Black Hole Thermodynamics.- 14.5. The Identification of a Black Hole—Cygnus X-1.- 14.6. The Possible Locale of the Occurrence of Black Holes.- 14.7. The Quasi-Steller Objects (Quasars).- 14.8. Gravitational Lens.- 15. Accretion onto Compact Objects.- 15.1. Introduction—Spherically Symmetric Accretion.- 15.2. Disk Accretion.- 15.3. Compact X-Ray Sources.- III. Cosmology.- 16. The Standard Cosmological Model.- 16.1. Introduction to the Friedmann Metric.- 16.2. Elementary Discussion of Standard Cosmology.- 16.3. The Observational Background of Cosmology.- 16.4. Summary.- 17. The Singularity Problem.- 17.1. Introduction.- 17.2. The Raychaudhuri Equation.- 17.3. The Meaning of Shear, Vorticity, and Expansion.- 17.4. An Elementary Singularity Theorem.- 17.5. The Gödel Universe.- 17.6. General Singularity Theorems.- 18. Thermal History of the Universe—Cosmological Nucleosynthesis.- 18.1. The Thermal History.- 18.2. Cosmological Nucleosynthesis.- 19. Structure Formation in the Universe.- 19.1. The Problem.- 19.2. The Linear Growth Formula.- 19.3. Finite Perturbation.- 19:4. Structure Formation with Dark Matter.- 20. Grand Unified Theory and Spontaneous Symmetry Breaking.- 20.1. Introduction.- 20.2. Gauge Fields.- 20.3. Weak Interaction.- 20.4. Strong Interaction and Grand Unification.- 20.5. Baryon Asymmetry and the Baryon/Photon Ratio.- 21. The Inflationary Scenario.- 21.1. Introduction.- 21.2. The Problems in Terms of Entropy.- 21.3. The Vacuum Energy—Stress Tensor and the de Sitter Phase.- 21.4. The Different Models of Inflation.- 21.5. A Critique of the Inflationary Models.- 21.6. Fluctuations in the Inflationary Models.- 22. Concluding Remarks.- Appendix. Differential Forms.- A.1. Introductory Ideas and Definitions.- A.2. Connection 1-Forms and Ricci Rotation Coefficients.- A.3. Cartan’s Equations of Structure.- A.4. Bianchi Identities and Symmetry Properties of the Riemann—Christoffel Tensor.- A.5. An Example of the Calculation of the Riemann—Christoffel Tensor.- References.