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Black holes : an introduction

Author: Derek J Raine; E G Thomas
Publisher: London : Imperial College Press, ©2005.
Edition/Format:   Print book : EnglishView all editions and formats
Database:WorldCat
Summary:
Providing an introduction to the fascinating subject of black holes, this book is suitable for advanced undergraduates and first year postgraduates. It offers an introduction to the exact solutions of Einstein's vacuum field equations, describing spherical and axisymmetric (rotating) black holes.
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Document Type: Book
All Authors / Contributors: Derek J Raine; E G Thomas
ISBN: 1860945880 9781860945885 1860945864 9781860945861
OCLC Number: 63195380
Description: xi, 155 pages : illustrations ; 23 cm
Contents: 1. Relativistic Gravity --
1.1. What is a black hole? --
1.2. Why study black holes? --
1.3. Elements of general relativity --
1.3.1. The principle of equivalence --
1.3.2. The Newtonian affine connection --
1.3.3. Newtonian gravity --
1.3.4. Metrics in relativity --
1.3.5. The velocity and momentum 4-vector --
1.3.6. General vectors and tensors --
1.3.7. Locally measured physical properties --
1.3.8. Derivatives in relativity --
1.3.9. Acceleration 4-vector --
1.3.10. Paths of light --
1.3.11. Einstein's field equations --
1.3.12. Symmetry and Killing's equation --
2. Spherical Black Holes --
2.1. The Schwarzschild metric --
2.1.1. Coordinates --
2.1.2. Proper distance --
2.1.3. Proper time --
2.1.4. Redshift --
2.1.5. Interpretation of M and geometric units --
2.1.6. The Schwarzschild radius --
2.1.7. The event horizon --
2.1.8. Birkoff's theorem --
2.1.9. Israel's theorem --
2.2. Orbits in Newtonian gravity --
2.2.1. Energy --
2.2.2. Angular momentum --
2.2.3. The Newtonian effective potential --
2.2.4. Classification of Newtonian orbits --
2.3. Particle orbits in the Schwarzschild metric --
2.3.1. Constants of the motion --
2.3.2. Energy --
2.3.3. Angular momentum --
2.3.4. The effective potential --
2.3.5. Newtonian approximation to the metric --
2.3.6. Classification of orbits --
2.3.7. Radial infall --
2.3.8. The locally measured energy of a particle --
2.3.9. Circular orbits --
2.3.10. Comparison with Newtonian orbits --
2.3.11. Orbital velocity in the frame of a hovering observer --
2.3.12. Energy in the last stable orbit --
2.4. Orbits of light rays --
2.4.1. Radial propagation of light --
2.4.2. Capture cross-section for light --
2.4.3. The view of the sky for a stationary observer --
2.5. Classical tests --
2.6. Falling into a black hole --
2.6.1. Free-fall time for a distant observer --
2.6.2. Light-travel time --
2.6.3. What the external observer sees --
2.6.4. An infalling observer's time --
2.6.5. What the infalling observer feels --
2.7. Capture by a black hole --
2.7.1. Case I: Capture of high angular momentum particles --
2.7.2. Case II: Capture of low energy particles --
2.8. Surface gravity of a black hole --
2.8.1. The proper acceleration of a hovering observer --
2.8.2. Surface gravity --
2.8.3. Rindler coordinates --
2.9. Other coordinates --
2.9.1. Null coordinates --
2.9.2. Eddington-Finkelstein coordinates --
2.10. Inside the black hole --
2.10.1. The infalling observer --
2.11. White holes --
2.12. Kruskal coordinates --
2.12.1. The singularities at r = 0 and cosmic censorship --
2.12.2. The spacetime of a collapsing star --
2.13. Embedding diagrams --
2.14. Asymptotic flatness --
2.14.1. The Penrose-Carter diagram for the Schwarzschild metric --
2.14.2. The Penrose-Carter diagram for the Newtonian metric --
2.15. Non-isolated black holes --
2.15.1. The infinite redshift surface --
2.15.2. Trapped surfaces --
2.15.3. Apparent horizon --
2.16. The membrane paradigm --
3. Rotating Black Holes --
3.1. The Kerr metric --
3.2. The event horizon --
3.2.1. The circumference of the event horizon --
3.2.2. The area of the event horizon --
3.3. Properties of the Kerr metric coefficients --
3.3.1. Identities --
3.3.2. Contravariant components --
3.4. Interpretation of m, a and geometric units --
3.5. Extreme Kerr black hole --
3.6. Robinson's theorem --
3.7. Particle orbits in the Kerr geometry --
3.7.1. Constants of the motion --
3.7.2. Energy --
3.7.3. Angular momentum --
3.7.4. The Carter integral --
3.7.5. The radial equation --
3.7.6. The effective potential --
3.8. Frame-dragging --
3.8.1. Orbits of zero angular momentum particles --
3.8.2. Orbits with non-zero angular momentum --
3.9. Zero angular momentum observers (ZAMOs) --
3.9.1. Some applications of ZAMOs --
3.10. Photon orbits --
3.10.1. The photon effective potential --
3.10.2. Azimuthal motion --
3.10.3. Photon capture cross-section --
3.11. The static limit surface --
3.12. The infinite redshift surface --
3.13. Circular orbits in the equatorial plane --
3.13.1. Innermost (marginally) stable circular orbit --
3.13.2. Period of a circular orbit --
3.13.3. Energy of the innermost stable orbit --
3.13.4. Angular momentum of the innermost stable orbit --
3.13.5. Marginally bound orbits --
3.13.6. Unbound orbits --
3.14. Polar orbits --
3.14.1. Orbital period --
3.15. The ergosphere --
3.15.1. Negative energy orbits --
3.15.2. Angular momentum of a negative energy particle --
3.15.3. The Penrose process --
3.15.4. Realising the Penrose process --
3.16. Spinning up a black hole --
3.16.1. From Schwarzschild to extreme Kerr black hole --
3.17. Other coordinates --
3.18. Penrose-Carter diagram --
3.18.1. Interior solutions and collapsing stars --
3.19. Closed timelike lines --
3.20. Charged black holes --
4. Black Hole Thermodynamics --
4.1. Black hole mechanics --
4.1.1. Surface gravity --
4.1.2. Redshift --
4.1.3. Conservation of energy --
4.2. The area of a Kerr black hole horizon cannot decrease --
4.2.1. Area change by accretion --
4.2.2. Area change produced by the Penrose process --
4.2.3. The area theorem --
4.2.4. Irreducible mass --
4.2.5. Maximum energy extraction --
4.2.6. Naked singularities --
4.3. Scattering of waves --
4.3.1. Superradiance --
4.4. Thermodynamics --
4.4.1. Horizon temperature --
4.4.2. The four laws of black hole thermodynamics --
4.5. Hawking radiation --
4.5.1. Introduction --
4.5.2. Casimir effect --
4.5.3. Thermal vacua in accelerated frames --
4.5.4. Hawking radiation --
4.6. Properties of radiating black holes --
4.6.1. Entropy and temperature --
4.6.2. Radiating black holes --
4.6.3. Black hole in a box --
4.7. Entropy and microstates --
5. Astrophysical Black Holes --
5.1. Introduction --
5.2. Stellar mass black holes --
5.2.1. Formation --
5.2.2. Finding stellar mass black holes --
5.2.3. The black hole at the centre of the Galaxy --
5.3. Supermassive black holes in other galaxies --
5.3.1. Intermediate mass black holes --
5.3.2. Mini black holes --
5.4. Further evidence for black hole spin --
5.5. Conclusions.
Responsibility: Derek Raine & Edwin Thomas.

Abstract:

Providing an introduction to the fascinating subject of black holes, this book is suitable for advanced undergraduates and first year postgraduates. It offers an introduction to the exact solutions  Read more...

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   schema:description "1. Relativistic Gravity -- 1.1. What is a black hole? -- 1.2. Why study black holes? -- 1.3. Elements of general relativity -- 1.3.1. The principle of equivalence -- 1.3.2. The Newtonian affine connection -- 1.3.3. Newtonian gravity -- 1.3.4. Metrics in relativity -- 1.3.5. The velocity and momentum 4-vector -- 1.3.6. General vectors and tensors -- 1.3.7. Locally measured physical properties -- 1.3.8. Derivatives in relativity -- 1.3.9. Acceleration 4-vector -- 1.3.10. Paths of light -- 1.3.11. Einstein's field equations -- 1.3.12. Symmetry and Killing's equation -- 2. Spherical Black Holes -- 2.1. The Schwarzschild metric -- 2.1.1. Coordinates -- 2.1.2. Proper distance -- 2.1.3. Proper time -- 2.1.4. Redshift -- 2.1.5. Interpretation of M and geometric units -- 2.1.6. The Schwarzschild radius -- 2.1.7. The event horizon -- 2.1.8. Birkoff's theorem -- 2.1.9. Israel's theorem -- 2.2. Orbits in Newtonian gravity -- 2.2.1. Energy -- 2.2.2. Angular momentum -- 2.2.3. The Newtonian effective potential -- 2.2.4. Classification of Newtonian orbits -- 2.3. Particle orbits in the Schwarzschild metric -- 2.3.1. Constants of the motion -- 2.3.2. Energy -- 2.3.3. Angular momentum -- 2.3.4. The effective potential -- 2.3.5. Newtonian approximation to the metric -- 2.3.6. Classification of orbits -- 2.3.7. Radial infall -- 2.3.8. The locally measured energy of a particle -- 2.3.9. Circular orbits -- 2.3.10. Comparison with Newtonian orbits -- 2.3.11. Orbital velocity in the frame of a hovering observer -- 2.3.12. Energy in the last stable orbit -- 2.4. Orbits of light rays -- 2.4.1. Radial propagation of light -- 2.4.2. Capture cross-section for light -- 2.4.3. The view of the sky for a stationary observer -- 2.5. Classical tests -- 2.6. Falling into a black hole -- 2.6.1. Free-fall time for a distant observer -- 2.6.2. Light-travel time -- 2.6.3. What the external observer sees -- 2.6.4. An infalling observer's time -- 2.6.5. What the infalling observer feels -- 2.7. Capture by a black hole -- 2.7.1. Case I: Capture of high angular momentum particles -- 2.7.2. Case II: Capture of low energy particles -- 2.8. Surface gravity of a black hole -- 2.8.1. The proper acceleration of a hovering observer -- 2.8.2. Surface gravity -- 2.8.3. Rindler coordinates -- 2.9. Other coordinates -- 2.9.1. Null coordinates -- 2.9.2. Eddington-Finkelstein coordinates -- 2.10. Inside the black hole -- 2.10.1. The infalling observer -- 2.11. White holes -- 2.12. Kruskal coordinates -- 2.12.1. The singularities at r = 0 and cosmic censorship -- 2.12.2. The spacetime of a collapsing star -- 2.13. Embedding diagrams -- 2.14. Asymptotic flatness -- 2.14.1. The Penrose-Carter diagram for the Schwarzschild metric -- 2.14.2. The Penrose-Carter diagram for the Newtonian metric -- 2.15. Non-isolated black holes -- 2.15.1. The infinite redshift surface -- 2.15.2. Trapped surfaces -- 2.15.3. Apparent horizon -- 2.16. The membrane paradigm -- 3. Rotating Black Holes -- 3.1. The Kerr metric -- 3.2. The event horizon -- 3.2.1. The circumference of the event horizon -- 3.2.2. The area of the event horizon -- 3.3. Properties of the Kerr metric coefficients -- 3.3.1. Identities -- 3.3.2. Contravariant components -- 3.4. Interpretation of m, a and geometric units -- 3.5. Extreme Kerr black hole -- 3.6. Robinson's theorem -- 3.7. Particle orbits in the Kerr geometry -- 3.7.1. Constants of the motion -- 3.7.2. Energy -- 3.7.3. Angular momentum -- 3.7.4. The Carter integral -- 3.7.5. The radial equation -- 3.7.6. The effective potential -- 3.8. Frame-dragging -- 3.8.1. Orbits of zero angular momentum particles -- 3.8.2. Orbits with non-zero angular momentum -- 3.9. Zero angular momentum observers (ZAMOs) -- 3.9.1. Some applications of ZAMOs -- 3.10. Photon orbits -- 3.10.1. The photon effective potential -- 3.10.2. Azimuthal motion -- 3.10.3. Photon capture cross-section -- 3.11. The static limit surface -- 3.12. The infinite redshift surface -- 3.13. Circular orbits in the equatorial plane -- 3.13.1. Innermost (marginally) stable circular orbit -- 3.13.2. Period of a circular orbit -- 3.13.3. Energy of the innermost stable orbit -- 3.13.4. Angular momentum of the innermost stable orbit -- 3.13.5. Marginally bound orbits -- 3.13.6. Unbound orbits -- 3.14. Polar orbits -- 3.14.1. Orbital period -- 3.15. The ergosphere -- 3.15.1. Negative energy orbits -- 3.15.2. Angular momentum of a negative energy particle -- 3.15.3. The Penrose process -- 3.15.4. Realising the Penrose process -- 3.16. Spinning up a black hole -- 3.16.1. From Schwarzschild to extreme Kerr black hole -- 3.17. Other coordinates -- 3.18. Penrose-Carter diagram -- 3.18.1. Interior solutions and collapsing stars -- 3.19. Closed timelike lines -- 3.20. Charged black holes -- 4. Black Hole Thermodynamics -- 4.1. Black hole mechanics -- 4.1.1. Surface gravity -- 4.1.2. Redshift -- 4.1.3. Conservation of energy -- 4.2. The area of a Kerr black hole horizon cannot decrease -- 4.2.1. Area change by accretion -- 4.2.2. Area change produced by the Penrose process -- 4.2.3. The area theorem -- 4.2.4. Irreducible mass -- 4.2.5. Maximum energy extraction -- 4.2.6. Naked singularities -- 4.3. Scattering of waves -- 4.3.1. Superradiance -- 4.4. Thermodynamics -- 4.4.1. Horizon temperature -- 4.4.2. The four laws of black hole thermodynamics -- 4.5. Hawking radiation -- 4.5.1. Introduction -- 4.5.2. Casimir effect -- 4.5.3. Thermal vacua in accelerated frames -- 4.5.4. Hawking radiation -- 4.6. Properties of radiating black holes -- 4.6.1. Entropy and temperature -- 4.6.2. Radiating black holes -- 4.6.3. Black hole in a box -- 4.7. Entropy and microstates -- 5. Astrophysical Black Holes -- 5.1. Introduction -- 5.2. Stellar mass black holes -- 5.2.1. Formation -- 5.2.2. Finding stellar mass black holes -- 5.2.3. The black hole at the centre of the Galaxy -- 5.3. 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