UFDF004 Relativistic Physics and Astrophysics II

Faculty of Philosophy and Science in Opava
Summer 2017
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
This course represents a continuation of UF/DF003 and brings an extension of mathematical methods of general relativity and it further expanses the astrophysical and cosmological applications of general relativity.
Syllabus
  • Selected problems of relativistic physics. Introduction to differential forms formalism, dual tensors, integration in spacetimes; integral form of conservation laws of energy and momentum, angular momentum tensor and spin; Fermi-Walker transfer and local reference frames; Lie derivation and Killing vectors; integration in curved spacetimes, Stokes rule, energy, momentum and angular momentum of gravitational field.
    Charged and rotating black holes. Reissner-Nordstrom geometry, inner and outer horizont, analytic continuation, complete Penrose diagram; Kerr geometry, naked singularities, Kerr-Schild and Boyer-Lindquist coordinates, event horizont and static limit surface, dragging of inertial frames; Kerr-Newman geometry, dipole electromagnetic field, mass, angular momentum and magnetic moment; Carter equations of motion, extraction of energy from ergosphere, superradiation, reversible and irreversible transformations, Penrose diagram of Kerr-Newman metrics, instability of the inner horizont.
    Properties of black holes. Wheeler's no hair theorem, uniqueness theorems, cosmic censorship hypothesis, singularity theorems.
    Black hole thermodynamics. Connection of geometrical and thermodynamical characteristics of black holes, four laws of black hole thermodynamics, Hawking quantum evaporation of black holes, black holes as thermodynamical systems.
    Standard cosmological model. Friedman equation and age of the Universe, equilibrium thermodynamics, entropy, thermal history of the Universe, causal horizont.
    Nuclear synthesis. Nuclear statistical equilibrium, initial conditions, creation of light elements, primordial nuclear synthesis as a test.
    Baryogenesis. Baryon asymmetry of the Universe, breaking of baryon symmetry, simple Boltzmann equation, vanishing of primordial asymmetries, lepton numbers in the Universe, non-equilibrium decay.
Literature
    recommended literature
  • Straumann, N. General Relativity. Springer, 2004. ISBN 3540219242. info
  • Börner G. The Early Universe. Springer, 2003. ISBN 3540441972. info
  • Wald R.M. General Relativity. The University of Chicago Press, 1984. ISBN 0226870324. info
  • Chandrasekhar S. The Mathematical Theory of Black Holes. Clarendon Press, 1983. ISBN 0-226-10100-2. info
  • Hawking S.W., Ellis, G. F. R. The Large Scale Structure of Space-Time. Cambridge Univ. Press, 1975. ISBN 0521200164. info
  • ] Misner C.W., Thorne K.S., Wheeler J.A. Gravitation. Freeman and Co., San Francisco, 1973. 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, Winter 2017, Summer 2018, Winter 2018, Summer 2019, Winter 2019, Summer 2020, Winter 2020, Summer 2021, Winter 2021, Summer 2022.
  • Enrolment Statistics (Summer 2017, recent)
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