TFNSP0001 Relativistic Physics and Astrophysics I

Institute of physics in Opava
winter 2024
Extent and Intensity
4/2/0. 8 credit(s). Type of Completion: zk (examination).
Teacher(s)
doc. RNDr. Jan Schee, Ph.D. (lecturer)
Mgr. Dmitriy Ovchinnikov (seminar tutor)
Guaranteed by
doc. RNDr. Jan Schee, Ph.D.
Institute of physics in Opava
Timetable
Tue 8:55–10:30 B4, Thu 10:35–12:10 F1
  • Timetable of Seminar Groups:
TFNSP0001/A: Tue 10:35–12:10 F1, D. Ovchinnikov
Prerequisites (in Czech)
(FAKULTA(FU) && TYP_STUDIA(N))
Course Enrolment Limitations
The course is also offered to the students of the fields other than those the course is directly associated with.
fields of study / plans the course is directly associated with
Course objectives
The course introduces to the students the advanced level of knowledge in relativistic physics and astrophysics including corresponding mathematical tool.
Learning outcomes
Passing the course a student will acquire following skills:
- mathematically correctly formulate relativistic physical problems
- solve relativistic problems
- solve Einstein equations in the framework of Cartan formulation of differential geometry
Syllabus
  • The key topics of the course:
    - Fundamentals of differential geometry. Manifold, coordinates, curve, vectors, tangent vector space, base vectors and 1-forms, tensors. Exterior derivative and differential forms. Connection, parallel transport, covariant derivative, geodesics.
    - Connection and curvature forms, Cartan equations. Metric and metric connection. Rieman tensor and its properties, Weyl tensor.
    - Tensor density, integral calculation in curved spacetime, Stokes theorem, Levi-Chivita theorem, integral form of energy and momentum conservation laws, angular momentum tensor and spin. Fermi-Walker transport and tetrade formalism.
    - Lie derivative and Killing vectors; spacetime symmetries.
    - Heuristic derivation of Einstein equations; derivation of Einstein equations from variation principle.
    - Covariant formulation of physical laws. Relativistic electrodynamics, geometric optics, hydrodynamics, thermodynamics and kinetic teory.
    - Gravitational waves. Linear theory of gravitation. Weak plane gravitational wave and its properties.
    - Generation of gravitational waves in linear theory, detection of gravitational waves. Wave fronts in exact theory, „Sandwich” wave. Petrov classification.
    - Vacuum spherically symmetric solution - Schwarzchild metric, derivation of Schwarzschild metric. Physical and coordinate singularity, Eddington-Finkelstein coordinates, Kruskal coordinates. Birkhoff theoerm.
    -Stellar structure equations: stress-energy tenzor for perfect fluid, Tolman-Oppenheimer-Volkoff equation, analytic solution for star with constant density.
    -Oppenheimer – Snyder gravitational collapse of dust sphere.
Literature
    recommended literature
  • Schutz, B. A First Course in General Relativity, 2nd ed Cambridge University Press, Cambridge, 2009
  • C. W. Misner, K. S. Thorne, J. A. Wheeler:. Gravitation. Freeman, San Francisco, 1973. info
  • Dvořák L. Obecná teorie relativity a moderní fyzikální obraz vesmíru, skriptum SPN, Praha, 1984
  • Bičák J., Ruděnko V. N. Teorie relativity a gravitační vlny, skriptum UK, Praha, 1986
  • S Chandrasekhar. The Mathematical Theory of Black Holes. Oxford University Press, 1998. info
  • Straumann, N. General Relativity and Reativistic Astrophysics, Springet-Verlag, Berlin, Heidelberg, New York, Tokyo 1984
  • Kuchař K. Základy obecné teorie relativity. Academia, 1968. info
  • Lightman A.P., Press W.H., Price R.H., Teukolsky S.A. Problem Book in Relativity and Gravitation. Princeton Univ. Press, Princeton, New Jersey, 1975. info
Teaching methods
Lectures. Discussing given problems. Solution of given exercises.
Assessment methods
oral exam, written test (75%)
Language of instruction
Czech
Further Comments
Study Materials
The course can also be completed outside the examination period.
The course is taught annually.
The course is also listed under the following terms winter 2020, winter 2021, winter 2022, winter 2023.
  • Enrolment Statistics (recent)
  • Permalink: https://is.slu.cz/course/fu/winter2024/TFNSP0001