Relativity Theory is an introduction into the concepts and mathematical methods of Einstein's theory. The first two parts are devoted to the special theory, while in Part 3 fundamentals of the general theory are summarized in simple terms. The mathematics relevant to this theory  is explained in detail in Part 4 no prior knowledge of the Riemannian geometry by the reader is, therefore, required. Part 5 contains those aspects of the theory which follow from the equivalance principle alone, Einstein-equations being introduced only in Part 6. Central symmetrical space-time and gravitational waves are treated in Parts 7 and 8 respectively. Part of the text is presented in the form of problems (there is about a hundred of them) each of which is accompanied with a detailed solution. The notes at the end of the book contain mainly historical material.

CONTENT

Foreword

Part 1. Special relativity (space-time geometry)

Reference frames.

Galilei-transformation.

The velocity of light and the relativity of simultaneity.

The general form of the transformation between systems of inerta.

The Lorentz-transformation and the relativistic addition of velocity.

Postulates of the relativity theory.

The notion of space-time.

Space-time geometry.

The notion of the proper time.

The causality paradox.

Lorentz-contraction.

Tensors.

Part 2. Special relativity (dynamics)

Velocity and acceleration.

Density and current-density.

Maxwell equations.

Geometrical optics

Motion of a point mass in a field of force

The momentum and energy of a point mass

Zero mass particles

The energy-momentum tensor

Spinors

Part 3. The gravity as geometry

Difficulties of the Newtonian theory of gravitation

The inertial and gravitational masses

The geodetic hypothesis

Locality of the inertial frames

Part 4. Riemannian geometry

Two-dimensional surfaces

The Riemannian manifold

The pseudoriemannian- manifold

Parallel transport

Covariant and absolute derivatives

Finite parallel transport

Geodetic equation

The concept of the curvature-tensor

Properties of the Riemann-tensor

Densities

Integration

Part 5. The pseudorimannian space-time and the principle of equivalence

Local frames of inertia

Nonrotating local accelerating frames  (Fermi coordinates)

The metrics around the Sun based on  the geodetic hypothesis

Electrodynamic in the pseudorimannian space-time

The gravitational red shift

Tetrads

Spinors in  pseudoriemannian space-time

Part 6. The Einstein equation

The Einstein equation

The Hilbert action

Gravitational energy

Coordinates in the general relativity

Part 7. Space-time around solitary stars

Central symmetric static space-time

The Schwarzschild-solution

Bending of light

Precession of the perihelion

Geodetic precession

The nature of the Schwarzschild.singularity

Kruskal-Szekeres space-time

The space-time of rotating stars.

Part 8. Gravitational radiation

Gravitational plane waves

Quadruple radiation

Principles of the detection of the gravitational radiation

Notes