- Cosmology - Science of the Universe in General. Conception of the Universe in Classical Physics.
Cosmological Paradoxes of Classical Cosmology. The Idea of Hierarchy as an Antithesis for Homogeneity.
Hierarchial Universe. Hubble Research of Galaxies Distribution. Modern Ideas of Hierarchial
Structure of the Universe. The Largest Scale of Heterogeneousness. Cosmological Principle. Formation of
Relativistic Cosmology.
- Space and Time. Newton Ideas about Space and Time. Classical Theory of Gravitation. Space-Time of
Special Theory of Relativity. Incompatibility of Special Theory of Relativity and Classical Theory of
Gravitation. Principle of Equivalence and General Principle of Relativity. Covariance of Physical Laws
Relative to Coordinates Transformation. Systems of Coordinates and Frames of Refernce. Idea of Space-Time
Curvature. Space-Time of General Theory of Relativity.
- Riemannian Geometry as a Mathematical Base of General Theory of Relativity. Differentiable Manifold.
Tensor Algebra. Tensor Fields on Manifold. Riemannian Manifold. Metric Tensor. Tensor Field Differentiation.
Covariant Derivative. Tensors of Curvature, Rici, Curvature Scalar.
- Paraller Transportation of Tensor Fields. Equation of Geodesics. Extreme Features of Geodesics. Equation
of Geodesics Deviation.
- Symmetry of Space-Time. Isometry, Groups of Isometry. Killing Vectors, Killing Equation. Maximum Order
of Isometry Groups. Constant Curvature Spaces. Maximum Symmetric Subspaces. Metric Tensor of Constant
Curvature Spaces.
- Tensor of Energy-Impulse(TEI). TEI of Ideal Liquid, Relativistic Liquid, Dust, Electro-Magnetic Field.
Einstein Tensor. Einstein Equation. Indeterminacy of Einstein Equation. Cosmological Λ-Term.
- The Simplest Solutions of Einstein Equations. Swarzschild External Solution. Geodesics in Swarzschild
Field. Effects of General Theory of Relativity in Solar System (Motion of Planet Perihelion, Deflection of
Light Rays, Gravitation Red Shift, Delay of Radar Echo). Experimental Test of Effects of General Theory of
Relativity. Swarzschild Black Hole.
- Weak Gravitation Field. Post-Newtonian Approximation. Relativistic Frames of References in Solar System.
Relativistic Astromery. Astronomical Scales of Time.
- Gravitational Waves. Analogy and Difference of Gravitation and Electromagnetic Waves. Possible Sources
of Gravitation Waves. Gravitation Wave Experiments. Cosmic Confirmation of Gravitation Waves.
- Various Cosmological Models. Main Cosmological Parameters (Hubble Constant, Deceleration Parameter,
Critical Density of Matter). Expanding Universe. Age of the Universe. Heterogenious Nonisotropic Models.
Models of the Universe with Rotation.
- The Most Widespread Distances in Cosmology (Photometric, Angular, Attendant, Intristic, Their
Dependence on Red Shift. Standard Tests of Cosmology. Ratio Dimension - Red Shift, Visible Magnitude -
Red Shift.
- Hubble Constant Determination. Cosmography of the Near Universe. Peculiar Velocities. Large-Scale
Streams in the Universe.
- Gravitation Lensing. Gravitation Lens Equation. Astrometric and Photometric Aspects of Lensing.
Microlensing. Weak Gravitational Lensing. Cosmic Distortion. Cosmological Parameters Determination from
Effects of Lensing.
- Hot Universe. Microwave Relic Radiation. Standard Scenario of the Universe Evolution. Cosmological
Singularity. Inflationary Universe. Initial Nucleo-Synthesis. Large-Scale Structures in the Universe and
Problem of Their Origin. Problem of Hidding Mass.Confirmation of Hot Universe Theory.
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