UFDF003 Relativistic Physics and Astrophysics I

Faculty of Philosophy and Science in Opava
Summer 2019
Extent and Intensity
0/0. 0 credit(s). Type of Completion: dzk.
Guaranteed by
prof. RNDr. Zdeněk Stuchlík, CSc.
Centrum interdisciplinárních studií – Faculty of Philosophy and Science in Opava
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 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
Czech
Further comments (probably available only in Czech)
The course can also be completed outside the examination period.
Teacher's information
The attendance at lectures is recommended. It can be substituted by
the self-study of recommended literature and individual consultations.
The course is also listed under the following terms Winter 2000, Summer 2001, Winter 2001, Summer 2002, Winter 2002, Summer 2003, Winter 2003, Summer 2004, Winter 2004, Summer 2005, Winter 2006, Summer 2007, Winter 2007, Summer 2008, Winter 2008, Summer 2009, Winter 2009, Summer 2010, Winter 2010, Summer 2011, Winter 2011, Summer 2012, Winter 2012, Summer 2013, Winter 2013, Summer 2014, Winter 2014, Summer 2015, Winter 2015, Summer 2016, Winter 2016, Summer 2017, Winter 2017, Summer 2018, Winter 2018, Winter 2019, Summer 2020, Winter 2020, Summer 2021, Winter 2021, Summer 2022.
  • Enrolment Statistics (Summer 2019, recent)
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