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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 | |
