# UOTR

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**Course:** Introduction to General Relativity

**Department/Abbreviation:** KEF/UOTR

**Year:** 2021

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

**Annotation:** The aim is to discuss the the basic ideas of the theory of gravitation and its position in the physical picture of the world, a historical development of opinions on gravitation, space and time, and to give a basicsummary of main starting points and predictions of theory of relativity.

**Course review:**

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Geometry and physics, theory of gravitation and its position in the physical picture of the world, historical development of opinions on gravitation, space and time, summary of main starting points and predictions of theory of relativity
Starting principle of general theory of relativity, Mach principle, principle of equivalence and its various formulations, Eötvös and Dicke experiments, principle of correspondence, principle of covariance, covariant notation of physical laws, gravitation as a curvature of spacetime.
Description of curved spacetime, coordinations, metrics, sign convention, local inertial systems, light cones, world lines, length, surface, volume, nesting diagram, vectors in the curved spacetime, equations of geodetic lines and integrals of motion (laws of conservation)
Geometry outside spherically symmetric stars, Schwartschild geometry, gravitational red shift, motion of test particles and photos (precession of perihelia of Mercury, diffraction of light in the gravitational field and delay of electromagnetic signals)
Experimental test in the Solar System, gravitational red shift, PPN parameters and their measurements
Relativistic phenomena in astrophysics, gravitational lenses, binary pulses, gravitational collapse and black holes, their observations in binary systems and in the centers of galaxies, Hawking evaporation of black holes
Gravitation around rotating objects, pulling of inertial systems, flywheels in curved spacetime and their precession, spacetime in the surrounding of rotating objects, Kerr geometry, motion in equatorial plane, ergosphere
Gravitational waves, linearized gravitational waves, detection of gravitational waves, energy and polarization of waves
Einstein equations, vectors, co-vectors, tensors, covariant differentiation, tidal forces, deviations of geodetic lines, tensor of torsion, law of conservation of energy and momentum, Einstein equations, Newton limit
Relativistic stars, Pauli principle, relativistic hydrostatic equilibrium, models of stars