It is not an exaggeration to say that one of the most exciting predictions of Einstein's theory of gravitation is that there may exist "black holes": putative objects whose gravitational fields are so strong that no physical bodies or signals can break free of their pull and escape. The proof that black holes do exist, and an analysis of their properties, would have a significance going far beyond astrophysics. Indeed, what is involved is not just the discovery of yet another even if extremely remarkable, astro physical object, but a test of the correctness of our understanding of the properties of space and time in extremely strong gravitational fields. Theoretical research into the properties of black holes, and into the possible corol laries of the hypothesis that they exist, has been carried out with special vigor since the beginning of the 1970's. In addition to those specific features of black holes that are important for the interpretation of their possible astrophysical manifestations, the theory has revealed a number of unexpected characteristics of physical interactions involving black holes. By the middle of the 1980's a fairly detailed understanding had been achieved of the properties of the black holes, their possible astrophysical manifestations, and the specifics of the various physical processes involved. Even though a completely reliable detection of a black hole had not yet been made at that time, several objects among those scrutinized by astrophysicists were considered as strong candidates to be confirmed as being black holes.

Inhalt
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.