# TRUA

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**Course:** Theory of Relativity and Astronomy

**Department/Abbreviation:** KEF/TRUA

**Year:** 2021

**Guarantee:** 'Mgr. Lukáš Richterek, Ph.D.'

**Annotation:** The aim of this module is to introduce students to the theory of relativity and the application of fundamental principles of relativistic physics in astrophysics and cosmology via selected particular examples. The section devoted to astronomy involves orientation in the sky and a description and explanation of the basic astronomical phenomena. Students should gain the necessary insight over this, which is at least for some secondary schools part of the curriculum.

**Course review:**

Introduction, space and time in non-relativistic physics, ether and basic experiments for its determination, Michelson-Morley experiment, Einstein postulates, Lorentz transformation and its consequences (length contraction, time dilatation, relativity of time and space, transformation of velocity)

Monkowski spacetime, event, space-time interval and true time, light cone, world line, causal structure of the spacetime, four-dimensional formalism and four-vectors, tensors in Minkowski spacetime and important operations with them, Minkowski diagram, covariance principle
Equations of relativistic dynamics of a particle, four-force and four-momentum, equivalence of mass and energy, basic equations of dynamics of a particle system, collisions and scattering of particles, stability of particles, bonding energy, annihilation of electron-pozitron pair, Compton scattering, tensor of angular momentum
Speeds over speed of light and causality principle, paradoxes, speeds under and over speed of light, paradox consequences of speeds over speed of light and tachyons, twin (time) paradox and other paradoxes, paradox of rotating disk and non-Euclidian geometry, relativistic aberration, relativistic Doppler effect, experimental verification of theory of relativity
Four-current and four-potential, Lorentz calibration condition, wave equations for field potentials, tensors of electromagnetic field and Maxwell equations, their transformations and field invariants, Lorentz four-force and its density, wave four-vector, tensor of energy and momentum of electromagnetic field, laws of conservation
Basics of general theory of relativity, principle of general covariance and principle of equivalence, introduction to tensor analysis in general metric spaces, Einstein equations of field, consequences of general theory of relativity