Preface.............................................................. 5 Introduction......................................................... 9 Chapter 1 Hydrodynamic limit - classical problems of accretion and ejection.... 13 1.1 Astrophysical introduction - accretion onto compact objects.... 13 1 1 1 Accretion disks........................................... 14 1.1.2 Standard model............................................ 17 1.1.3 ADAF, ADIOS, etc.......................................... 20 1.2 Basic properties of transonic hydrodynamical flows............. 22 1.2.1 Basic equations........................................... 22 1.2.2 Spherically symmetric flow................................ 24 1.2.3 Plane potential flow...................................... 27 1.3 Axisymmetric stationary flows - nonrelativistic case........... 34 1.3.1 Basic equations........................................... 34 1.3.2 Mathematical interlude - covariant language............... 35 1.3.3 Structure of the two-dimensional flow..................... 37 1.3.4 Bondi-Hoyle accretion..................................... 45 1.3.5 Ejection from slowly rotating star........................ 49 1.4 Axisymmetric stationary accretion onto black hole.............. 57 1.4.1 Physical interlude - (3+1)-split in the Kerr metric....... 57 1.4.2 Basic equations........................................... 61 1.4.3 Exact solutions........................................... 65 1.4.4 Bondi-Hoyle accretion - relativistic limit................ 67 1.4.5 Accretion onto slowly rotating black hole................. 70 1.4.6 Accretion of a gas with small angular momentum onto nonrotating black hole......... 71 1.4.7 Thin transonic disk....................................... 77 1.5 Conclusion..................................................... 87 1 Chapter 2 Force-free limit - radio pulsar magnetosphere........................ 89 2.1 Astrophysical introduction..................................... 89 2.2 Main physical processes........................................ 92 2.2.1 Vacuum approximation...................................... 92 2.2.2 Particle creation in a strong magnetic field.............. 96 2.2.3 Structure of the magnetosphere............................ 99 2.3 Generation of secondary plasma.................................104 2.3.1 'Internal gap'............................................104 2.3.2 Neutron star surface......................................109 2.3.3 Propagation of gamma-quanta in superstrong magnetic field......................110 2.3.4 Effects of the general relativity.........................111 2.3.5 Particle generation in the magnetosphere................. 113 2.3.6 'Hollow cone' model...................................... 114 2.3.7 Particle generation - 'external gap'..................... 119 2.4 Pulsar equation............................................... 119 2.4.1 Force-free approximation. Magnetization parameter........ 119 2.4.2 Electromagnetic field. Integrals of motion............... 121 2.4.3 Grad-Shafranov equation.................................. 124 2.4.4 Mathematical interlude - quasi stationary approach....... 127 2.5 Energy loss of radio pulsars.................................. 130 2.5.1 Current loss mechanism................................... 130 2.5.2 Braking of inclined and orthogonal rotator............... 133 2.6 Structure of the magnetosphere................................ 141 2.6.1 Exact solutions.......................................... 141 2.6.2 Structure of the magnetosphere with longitudinal currents 158 2.6.3 Models of th