Infopaket

Relativistic theory of gravity

ВК 1

Вибіркова дисципліна для ОП

First

2023/2024

5 Semester

3

Know the basic elements of tensor analysis. Know Einstein's equations and methods for solving them. Know the methods of experimental verification of the general theory of relativity and the basic properties of the Schwarzschild solution and the standard cosmological model. Be able to calculate the components of the Riemann curvature tensor. Be able to perform the transformation of tensor quantities between different coordinate systems. Be able to find solutions to geodetic equations and Einstein's equations. Present the results of independent work in writing or orally Process information from various sources, organize it and apply it in practical tasks

Full-time form

1. Know the basic principles of tensor analysis; properties of Einstein's equations and methods of their solution; methods of experimental verification of the general theory of relativity and the main properties of the Schwarzschild solution and the standard cosmological model. 2. Be able to calculate the components of the Riemann curvature tensor, perform the transformation of tensor quantities between different coordinate systems; find solutions to geodetic equations and Einstein's equations. 3. Have basic skills in constructing and solving relativistic Einstein equations for the gravitational field.

Мodule 1 Fundamentals of Riemannian geometry 1 Fundamentals of tensor analysis 2 Covariant derivative and Riemann curvature tensor 3 Einstein's equation Мodule 2 Solutions of Einstein's equations and elements of cosmology 4 Schwarzschild metric 5 Gravitational waves 6 Properties of cosmological solutions

Основна: (Базова) 1. Y. Shtanov, “Notes on General Relativity”, http://shtanov.pp.ua/gravity/GR-notes.pdf 2. S. Carrol, “Spacetime and Geometry, An Introduction to General Relativity”, The University of Chikago Press, Chikago, 2003. 3. R. M. Wald, “General Relativity”, The University of Chikago Press, Chikago, 1984. 4. В. I. Жданов, Вступ до теорiї вiдносностi, ВПЦ “Київський унiверситет” (2008). Додаткова: 1. M. Blau, “Lecture notes on General Relativity”, http://www.blau.itp.unibe.ch/Lecturenotes.html

Lectures Practical Advice Individual work

Homeworks Exam work

Ukrainian