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Preface | |

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Relativistic Gravity | |

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What is a black hole? | |

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Why study black holes? | |

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Elements of general relativity | |

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The principle of equivalence | |

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The Newtonian affine connection | |

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Newtonian gravity | |

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Metrics in relativity | |

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The velocity and momentum 4-vector | |

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General vectors and tensors | |

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Locally measured physical quantities | |

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Derivatives in relativity | |

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Acceleration 4-vector | |

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Paths of light | |

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Einstein's field equations | |

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Symmetry and Killing's equation | |

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Spherical Black Holes | |

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The Schwarzschild metric | |

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Coordinates | |

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Proper distance | |

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Proper time | |

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Redshift | |

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Interpretation of M and geometric units | |

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The Schwarzschild radius | |

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The event horizon | |

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Birkoff's theorem | |

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Israel's theorem | |

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Orbits in Newtonian gravity | |

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Newtonian Energy | |

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Angular momentum | |

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The Newtonian effective potential | |

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Classification of Newtonian orbits | |

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Particle orbits in the Schwarzschild metric | |

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Constants of the motion | |

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Conserved Energy | |

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Angular momentum | |

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The effective potential | |

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Newtonian approximation to the metric | |

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Classification of orbits | |

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Radial infall | |

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The locally measured energy of a particle | |

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Circular orbits | |

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Comparison with Newtonian orbits | |

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Orbital velocity in the frame of a hovering observer | |

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Energy in the last stable orbit | |

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Orbits of light rays | |

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Radial propagation of light | |

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Capture cross-section for light | |

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The view of the sky for a stationary observer | |

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Classical tests | |

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Palling into a black hole | |

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Free-fall time for a distant observer | |

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Light-travel time | |

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What the external observer sees | |

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An infalling observer's time | |

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What the infalling observer feels | |

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Capture by a black hole | |

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Case I: Capture of high angular momentum particles | |

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Case II: Capture of low energy particles | |

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Surface gravity of a black hole | |

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The proper acceleration of a hovering observer | |

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Surface gravity | |

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Rindler coordinates | |

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Other coordinates | |

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Null coordinates | |

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Eddington-Finkelstein coordinates | |

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Inside the black hole | |

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The infalling observer | |

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White holes | |

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Kruskal coordinates | |

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The singularities at r = 0 and cosmic censorship | |

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The spacetime of a collapsing star | |

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Embedding diagrams | |

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Asymptotic flatness | |

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The Penrose-Carter diagram for the Schwarzschild metric | |

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The Penrose-Carter diagram for the Newtonian metric | |

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Non-isolated black holes | |

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The infinite redshift surface | |

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Trapped surfaces | |

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Apparent horizon | |

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The membrane paradigm | |

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Rotating Black Holes | |

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The Kerr metric | |

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The event horizon | |

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The circumference of the event horizon | |

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The area of the event horizon | |

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Properties of the Kerr metric coefficients | |

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Identities | |

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Contravariant components | |

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Interpretation of m, a and geometric units | |

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Extreme Kerr black hole | |

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Robinson's theorem | |

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Particle orbits in the Kerr geometry | |

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Constants of the motion | |

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Energy | |

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Angular momentum | |

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The Carter integral | |

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The radial equation | |

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The effective potential | |

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Frame-dragging | |

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Free fall with zero angular momentum | |

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Orbits with non-zero angular momentum | |

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Zero angular momentum observers (ZAMOs) | |

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Some applications of ZAMOs | |

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Photon orbits | |

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The photon effective potential | |

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Azimuthal motion | |

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Photon capture cross-section | |

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The static limit surface | |

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The infinite redshift surface | |

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Circular orbits in the equatorial plane | |

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Innermost (marginally) stable circular orbit | |

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Period of a circular orbit | |

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Energy of the innermost stable orbit | |

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Angular momentum of the innermost stable orbit | |

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Marginally bound orbits | |

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Unbound orbits | |

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Polar orbits | |

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Orbital period | |

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The ergosphere | |

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Negative energy orbits | |

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Energy and angular momentum | |

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The Penrose process | |

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Realising the Penrose process | |

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Spinning up a black hole | |

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From Schwarzschild to extreme Kerr black hole | |

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Other coordinates | |

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Penrose-Carter diagram | |

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Interior solutions and collapsing stars | |

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Closed timelike lines | |

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Charged black holes | |

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Black Hole Thermodynamics | |

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Black hole mechanics | |

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Surface gravity | |

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Redshift | |

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Conservation of energy | |

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The area of a Kerr black hole horizon cannot decrease | |

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Area change by accretion | |

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Area change produced by the Penrose process | |

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The area theorem | |

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Irreducible mass | |

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Maximum energy extraction | |

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Naked singularities | |

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Scattering of waves | |

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Superradiance | |

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Thermodynamics | |

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Horizon temperature | |

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The four laws of black hole thermodynamics | |

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Hawking radiation | |

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Introduction | |

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Casimir effect | |

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Thermal vacua in accelerated frames | |

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Hawking radiation | |

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Properties of radiating black holes | |

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Entropy and temperature | |

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Radiating black holes | |

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Black hole in a box | |

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Entropy and microstates | |

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Wormholes and Time Travel | |

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Introduction | |

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Wormholes | |

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Traversible wormholes | |

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Creating a wormhole | |

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Weak energy condition | |

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Exotic matter | |

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Time machines | |

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Chronology protection | |

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Astrophysical Black Holes | |

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Introduction | |

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Stellar mass black holes | |

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Formation | |

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Finding stellar mass black holes | |

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The black hole at the centre of the Galaxy | |

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Supermassive black holes in other galaxies | |

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Intermediate mass black holes | |

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Mini black holes | |

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Further evidence for black hole spin | |

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Conclusions | |

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Solutions to Problems | |

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References | |

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Bibliography | |

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Index | |