UFTF206 Relativistic Physics and Astrophysics I

Faculty of Philosophy and Science in Opava
Winter 2013
Extent and Intensity
4/2/0. 8 credit(s). Type of Completion: zk (examination).
Teacher(s)
prof. RNDr. Zdeněk Stuchlík, CSc. (lecturer)
doc. RNDr. Jan Schee, Ph.D. (seminar tutor)
Guaranteed by
prof. RNDr. Zdeněk Stuchlík, CSc.
Centrum interdisciplinárních studií – Faculty of Philosophy and Science in Opava
Course Enrolment Limitations
The course is offered to students of any study field.
Course objectives
The basic ideas of general relativity are given, including the relevant parts of differential geometry. They are completed by the basical applications of general relativity in astrophysics and cosmology.
Syllabus
  • Evolution of ideas about space, time and Universe. Euclid, Aristotle, Copernicus, Kepler, Galileo, Newton, Einstein.
    Special theory of relativity and gravitational law. Minkowski spacetime, Lorentz transformation, equations of motion, Maxwell equations, energy-momentum tensor, conservation laws, Milne universe, Rindler universe, Nordstrom theory of gravitation.
    Basic principles of general relativity. Principle of equivalence, its experimental tests and consequences, principle of general covariance, general coordinate systems, free particle motion.
    Geometry of curved spacetimes. Metric, covariant and contravariant tensors, parallel transport, absolute derivation, affine connection, Christoffel symbols, geodesics, Reimann curvature tensor and Einstein tensor, Killing vectors, geodesic deviation equation.
    Basic laws of general relativity. General covariance of physical laws in curved spacetimes, principle of minimal action, conservation laws, Einstein gravitational law, cosmological constant, properties of Einstein equations, Schwarzschild solution of Einstein equations, particle and proton motion in the Schwarzschild geometry, Binet formula.
    Tests of general relativity, Brans-Dicke and other alternative theories of gravity, gravitational redshift, perihélium shift, deflection of light, delay of signals in gravitational fields, gravitational lenses.
    Weak gravitational waves, weak plane gravitational wave, linearized gravitational equations, physical properties of plane gravitational waves (interaction with test particles, helicity, polarization, energy transfer), generation of gravitational waves in linearized theory, astrophysical sources (binary systems, PSR 1913+16, rotating pulsars), methods of detection.
    Stellar structure, Stellar equilibrium, Tolman-Oppenheimer-Volkoff equation of hydrostatic equlibrium,
    nuclear reactions, energy transfer, equations of state, models of internal structure of stars, creation and evolution of stars.
    Gravitational collapse and black holes. Gravitational radius as an event horizont, R and T regions of the Schwarzschild geometry, physical singularity, Lemaitre and Kruskal coordinates, Einstein-Rosen bridge, white holes, gravitational collapse of stars, tidal forces in vicinity of black holes, observation of black holes.
    Structure and evolution of the Universe. Homogeneity and isotropy of the Universe, cosmological principle, Seeliger and Olbers paradox of static universe, Hubble law, Robertson-Walker metric, energy-momentum tensor of matter in the Universe, conservation law, equations of state, Einstein equations, Friedman models, cosmological redshift, Hubble and decelleration parameters, relict radiation.
Literature
    recommended literature
  • Bičak I., Rudenko V. N. Gravitacionnye volny v OTO i problema ich obnaruženija (Existují česká skripta MFF UK v Praze). Izdatelstvo Moskovskogo universiteta, Moskva, 1987. info
  • Schutz B.F. A first course in general relativity. Cambridge University Press, 1984. ISBN 0 521 27703 5. info
  • Shapiro S.L., Teukolski S.A. Black Holes, White Dwarfs, and Neutron Stars. The Physics of Compact Objects. A Wiley-Interscience Publication. John Wiley & Sons Inc., 1983. ISBN 978-0-471-87316-7. info
  • Rindler W. Essential Relativity. Special, General, and Cosmology. Revised 2nd Edition. Springer, 1977. ISBN 978-3-540-07970-5. 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
  • ] Misner C.W., Thorne K.S., Wheeler J.A. Gravitation. Freeman and Co., San Francisco, 1973. info
  • Landau L.D., Lifšic E.M. Teoretičeskaja fizika II. Teorija polja. Nauka, Moskva, 1973. info
  • Kuchař K. Základy obecné teorie relativity. Academia, 1968. info
Language of instruction
English
Further comments (probably available only in Czech)
The course can also be completed outside the examination period.
Teacher's information
60% attendance at lectures
  • Enrolment Statistics (recent)
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