The geometry of special and general relativity and some physical applications

The geometry of special and general relativity and some physical applications The consequences of the indefinite metric of Minkowsky space−time making its geometry more counterintuitive than curved non-Euclidean spaces are discussed. The Pythagorean theorem occurs sometimes to be different from the usual one leading to such consequences as the twin paradox, mass defect, etc. Properties of intervals and world lines, as well as elementary particles as different representations of the Poincare group, are discussed. Time loops as “time machines” are mentioned. In general, relativity one must mention the great intuition of Einstein that Newtonian gravity is the property of the curvature of time but not of space. Last discoveries in gravitation physics such as registration of gravitational waves and the black hole shadow are discussed as well as problems of singularities and horizons.