Fundamental principles of general theory of relativity; principle of equivalence, principle of general covariance. Parallel transport. Geodesics. Time dilation and frequency shift in a gravitational field. Covariant derivative. Curvature, the Riemann tensor. Energy-momentum tensor (ideal fluid). Einstein field equations. Lie derivative and space-time symmetries. Schwarzschild solution of Einstein's equations. Homogeneous and isotropic cosmological models.
Introductory course of general theory of relativity. The only specific knowledge assumed is the real four-dimensional tensor formalism (namely the abstract-index formalism) -- the same we were using in the special-relativity course. It is not necessary to know differential geometry in advance, we will introduce the necessary notions along the way.
Thursday 10:40-12:55, T1 lecture room (MFF Trója).
In 2021/22, the course is being taught live in Czech, with streming switched on (but not recorded) ... link: https://www.mff.cuni.cz/cs/verejnost/multimedia/t1-stream.
Videos from 2020/21 English run are linked below. (Please note there is also an "official" recording in Czech at Faculty webpages https://is.mff.cuni.cz/prednasky.)
Examinantion in Czech as well as in English may be chosen. Any feedback welcome (email: email@example.com).
Time dilation and frequency shift
Riemann tensor; Ideal fluid
Hydrostatic equilibrium; Einstein field equations
Einstein equations; Principle of minimal coupling
Introduction -- popular summary of GR
Lie derivative and space-time symmetries
Geodesic motion in Schwarzschild field
Cosmology -- FLRW metrics, cosmic fluid
Cosmological redshift; Friedmann equation and cosmic evolution