Reference Frame and Lorentz Transformation

Abstract

Generalization of an idea may lead to very interesting result. I considered in the paper the concept of reference frame in general relativity and geometry of metric- affinne manifold. Using this concept I learn few physical applications: Lorentz transformation in gravitational fields, Doppler shift. A reference frame in event space is a smooth field of orthonormal bases. Every reference frame is equipped by anholonomic coordinates. Using anholonomic coordinates allows to find out relative speed of two observers and appropriate Lorentz transformation. Synchronization of a reference frame is an anholonomic time coordinate. Simple calculations show how synchronization influences time measurement in the vicinity of the Earth. Measurement of Doppler shift from the star orbiting the black hole helps to determine mass of the black hole. According observations of Sgr A, if non orbiting observer estimates age of S2 about 10 Myr, this star is 0.297 Myr younger. We call a manifold with torsion the metric-affine manifold. We cannot draw closed parallelogram in event space, if there exists torsion. Learning how torsion influences on tidal force reveals similarity between tidal equation for geodesic and the Killing equation of second type. The relationship between tidal acceleration, curvature and torsion gives an opportunity to measure torsion.