Mathematical Structure of Time and Space II
No description for this lecture
March 2, 2020
8 a.m. - 10 a.m.
What is gravity?; First law of dynamics: global and local inertial frames
March 9, 2020
8 a.m. - 10 a.m.
What is a local frame of reference; Description of the reference system using connection coefficients
March 16, 2020
8 a.m. - 10 a.m.
Equation of a line in a spherical coordinate system; Curvature tensor
March 23, 2020
8 a.m. - 10 a.m.
Riemann tensor. Principles of "least action"; Variational principles in field theory and control theory
March 30, 2020
8 a.m. - 10 a.m.
About the fact that in dynamic field theories it is not allowed to determine a priori the value of the field at the boundary; Variational formulation of electrodynamics. Covariant derivative I.
April 6, 2020
8 a.m. - 10 a.m.
Covariant derivative II. Examples and applications.; Levi-Civity connection or "metric connection"
April 13, 2020
8 a.m. - 10 a.m.
The geodesic is the great circle of a metric connection; Decomposition of the curvature tensor into irreducible components
April 20, 2020
8 a.m. - 10 a.m.
Derivation of the dynamics of the gravitational field from the variational principle; Metrics enter the arena
April 27, 2020
8 a.m. - 10 a.m.
Einstein's vacuum equations. Cosmological constant; Einstein's equations in the presence of matter
May 4, 2020
8 a.m. - 10 a.m.
Properties of the metric Riemann tensor; Derivation of gravitational field equations using the Hilbert method
May 11, 2020
8 a.m. - 10 a.m.
Three different ways of deriving Einstein's equations from the variational principle; Three variation rules - completion. Introduction to the linear theory of gravity
May 18, 2020
8 a.m. - 10 a.m.
A linear approximation of Einstein's theory of gravity; Spherically symmetric configurations of the gravitational field
May 25, 2020
8 a.m. - 10 a.m.
External curvature. Theorem Gauss-Codazzi
June 1, 2020
8 a.m. - 10 a.m.
Schwarzschild metric; Surprising properties of Schwarzschild's solution. Black holes
June 8, 2020
8 a.m. - 10 a.m.
Outskirts: gravitational waves, cosmological models, quantization; Outskirts: graviton, unification, black matter
Declaration of Accessibility
Software development:
Andrzej Sawicki
Polish National Agency for Academic Exchange
The Project is financed by the Polish National Agency for Academic Exchange under the Foreign Promotion Programme