Black Hole Physics

I Basic Concepts.- 1 Introduction: Brief History of Black Hole Physics.- 2 Spherically Symmetric Black Holes.- 3 Rotating Black Holes.- 4 Black hole Perturbations (Written jointly with N. Andersson).- 5 General Properties of Black Holes.- 6 Stationary Black Holes.- 7 Physical Effects in the Gravitational Field of a Black Hole.- 8 Black Hole Electrodynamics.- >9 Astrophysics of Black Holes.- II Further Developments.- 10 Quantum Particle Creation by Black Holes.- 11 Quantum Physics of Black Holes.- 12 Thermodynamics of Black Holes.- 13 Black Holes in Unified Theories.- 14 The Interior of a Black Hole.- 15 Ultimate Fate of Black and White Holes.- 16 Black Holes, Wormholes, and Time Machines.- Conclusion.- Appendices.- A Mathematical Formulas.- A.1 Differential Manifold. Tensors.- A.2 Metric. Space and Time Intervals.- A.3 Causal Structure.- A.4 Covariant Derivative.- A.5 Geodesic Lines.- A.6 Curvature.- A.7 Lie- and Fermi-Transport.- A.8 Symmetries and Conservation Laws.- A.9 Geometry of Congruence of Lines.- A.10 Stationary Congruences.- A.10.1 Killing congruence.- A.10.2 Congruence of locally non-rotating observers.- A.11 Local Reference Frames.- A.12 Geometry of Subspaces.- A.13 Integration in Curved Space.- A.14 Conformai Transformations.- A.15 Einstein Equations.- B Spherically Symmetric Spacetimes.- B.1 Spherically Symmetric Geometry.- B.2 Reduced Action.- B.3 Generalized Birkhoff’s Theorem.- B.4 Spherically Symmetric Vacuum Solutions.- B.4.1 Schwarzschild metric.- B.4.2 Scaling properties.- B.5 Kruskal Metric.- B.5.1 Derivation of Kruskal metric.- B.5.2 Relation between Kruskal and Schwarzschild metrics.- B.5.3 Kruskal spacetime as maximal analytical continuation of the Schwarzschild metric.- B.5.4 Einstein-Rosen bridge.- B.6 Tolman Solution.- C Rindler Frame inMinkowski Spacetime.- C.1 Uniformly Accelerated Motion.- C.2 Rindler Frame.- C.3 Light and Particle Propagation.- C.4 Maximal Analytical Extension of Rindler Spacetime.- D Kerr-Newman Geometry.- D.1 Kerr-Newman Metric.- D.2 Christoffel Symbol.- D.3 Symmetries.- D.4 Motion of Test Particles.- D.4.1 Integrals of motion.- D.4.2 Hamilton-Jacobi method.- D.5 Stationary Congruences in the Kerr-Newman Geometry.- D.5.1 Killing congruence.- D.5.2 Congruence of locally non-rotating observers.- D.6 Algebraic Properties.- D.7 Analytic Extension.- E Newman-Penrose Formalism.- E.1 Complex Null Tetrad. Spin Coefficients.- E.2 Covariant Derivatives. Ricci and Weyl Tensor.- E.3 Newman-Penrose Equations.- E.4 Bianchi Identities.- F Wave Fields in a Curved Spacetime.- F.1 Scalar Field.- F.2 Electromagnetic Field.- F.3 Gravitational Perturbations.- G Wave Fields in the Kerr Metric.- G.1 Teukolsky Equation.- G.2 Separation of Variables. Spin-Weighted Spheroidal Harmonics.- G.3 Radial Equation.- G.4 Massless Scalar Field.- G.5 Electromagnetic Field.- G.6 Gravitational Perturbations.- H Quantum Fields in Kerr Spacetime.- H.1 Quantum Theory in an External Field.- H.2 Vacuum. Many-Particle States.- H.4 Massless Fields Quantization in Kerr Spacetime.- H.6 Averaging over “Non-observable” States.- I Quantum Oscillator.- 1.1 Action.- 1.2 Quantization and Representations.- 1.3 Quantum Oscillator at Finite Temperature.- 1.4 Two Mode Coupled Oscillators.