Black Holes: Big Picture / 1: |
Gravity and Black Holes / 1.1: |
Brief History of Black Holes / 1.2: |
'Dark Stars' vs. Black Holes / 1.3: |
Final State of Stellar Evolution / 1.4: |
Equilibrium of Gravitating Systems / 1.5: |
Important Notions of Astrophysics / 1.6: |
Black Holes in Astrophysics and Cosmology / 1.7: |
Stellar-Mass Black Holes / 1.8: |
Supermassive Black Holes / 1.9: |
Primordial Black Holes / 1.10: |
Black Holes in Theoretical Physics / 1.11: |
Black Holes and Extra Dimensions / 1.12: |
Physics in a Uniformly Accelerated Frame / 2: |
Minkowski Spacetime and Its Symmetries / 2.1: |
Minkowski Spacetime in Curved Coordinates / 2.2: |
Uniformly Accelerated Reference Frame / 2.3: |
Homogeneous Gravitational Field / 2.4: |
Causal Structure / 2.5: |
Wick's Rotation in the Rindler Space / 2.6: |
Riemannian Geometry / 3: |
Differential Manifold. Tensors / 3.1: |
Metric / 3.2: |
Covariant Derivative / 3.3: |
Lie and Fermi Transport / 3.4: |
Curvature Tensor / 3.5: |
Parallel Transport of a Vector / 3.6: |
Spacetime Symmetries / 3.7: |
Submanifold / 3.8: |
Integration / 3.9: |
Particle Motion in Curved Spacetime / 4: |
Equations of Motion / 4.1: |
Phase Space / 4.2: |
Complete Integrability / 4.3: |
Einstein Equations / 5: |
Einstein-Hilbert Action / 5.1: |
Linearized Gravity / 5.2: |
Gravitational radiation / 5.4: |
Gravity in Higher-Dimensions / 5.5: |
Spherically Symmetric Black Holes / 6: |
Spherically Symmetric Gravitational Field / 6.1: |
Schwarzschild-de Sitter Metric / 6.2: |
Global Structure of the Schwarzschild Spacetime / 6.3: |
Black Hole Interior / 6.4: |
Painleve-Gullstrand Metric / 6.5: |
Eddington-Finkelstein Coordinates / 6.6: |
Charged Black Holes / 6.7: |
Higher-Dimensional Spherical Black Holes / 6.8: |
Particles and Light Motion in Schwarzschild Spacetime / 7: |
Particle Trajectories / 7.1: |
Kepler's Law / 7.3: |
Light Propagation / 7.4: |
Ray-Tracing in Schwarzschild Spacetime / 7.5: |
Black Hole as a Gravitational Lens / 7.6: |
Radiation from an Object Moving Around the Black Hole / 7.7: |
Equations of Motion in 'Tilted' Spherical Coordinates / 7.8: |
Magnetized Schwarzschild Black Hole / 7.9: |
Particle and Light Motion Near Higher-Dimensional Black Holes / 7.10: |
Rotating Black Holes / 8: |
Kerr Spacetime / 8.1: |
Ergosphere. Horizon / 8.2: |
Particle and Light Motion in Equatorial Plane / 8.3: |
Spinning up the Black Hole / 8.4: |
Geodesies in Kerr Spacetime: General Case / 8.5: |
Hidden Symmetries of Kerr Spacetime / 8.6: |
Energy Extraction from a Rotating Black Hole / 8.8: |
Black Holes in External Magnetic Field / 8.9: |
Classical and Quantum Fields near Black Holes / 9: |
Introduction / 9.1: |
Static Field in the Schwarzschild Spacetime / 9.2: |
Dimensional Reduction / 9.3: |
Quasinormal Modes / 9.4: |
Massless Fields in the Kerr Spacetime / 9.5: |
Black Hole in a Thermal Bath / 9.6: |
Hawking Effect / 9.7: |
Quantum Fields in the Rindler Spacetime / 9.8: |
Black Hole Thermodynamics / 9.9: |
Higher-Dimensional Generalizations / 9.10: |
Black Holes and All That Jazz / 10: |
Asymptotically Flat Spacetimes / 10.1: |
Black Holes: General Definition and Properties / 10.2: |
Black Holes and Search for Gravitational Waves / 10.3: |
'Black Holes' in Laboratories / 10.4: |
Black Holes in Colliders? / 10.5: |
Higher-Dimensional Black Holes / 10.6: |
Wormholes / 10.7: |
'Time Machine' Problem / 10.8: |
Fundamental Constants and Units / Appendix A: |
Fundamental Constants / A.1: |
Planck Units / A.2: |
Conversion Factors / A.3: |
Various Scales of Masses / A.4: |
Milky Way Galaxy Observational Data / A.5: |
Universe Observational Data / A.6: |
Dimensionless Entropy (S/kb) / A.7: |
Gauss-Codazzi Equations / Appendix B: |
Static Surface in a Static Spacetime / B.1: |
Conformal Transformations / Appendix C: |
Hidden Symmetries / Appendix D: |
Conformal Killing Tensor / D.1: |
Killing-Yano Tensors / D.2: |
Primary Killing Vector / D.3: |
Properties of the Primary Killing Vector / D.4: |
Secondary Killing Vector / D.5: |
Darboux Basis / D.6: |
Canonical Form of Metric / D.7: |
Separation of Variables in Canonical Coordinates / D.8: |
Higher-Dimensional Kerr-NUT-(A)dS Metric / D.9: |
Boundary Term for the Einstein-Hilbert Action / Appendix E: |
An Example Illustrating the Problem / E.1: |
Boundary Term for the Euclidean Einstein-Hilbert Action / E.2: |
Quantum Fields / Appendix F: |
Classical Oscillator / F.1: |
Quantum Oscillator / F.2: |
Quantum Field in Flat Spacetime / F.3: |
Quantum Theory in (1+1)-Spacetime / F.4: |
References |
Index |
Black Holes: Big Picture / 1: |
Gravity and Black Holes / 1.1: |
Brief History of Black Holes / 1.2: |
'Dark Stars' vs. Black Holes / 1.3: |
Final State of Stellar Evolution / 1.4: |
Equilibrium of Gravitating Systems / 1.5: |