MU03256 Mathematical Foundations of the General Theory of Relativity I

Mathematical Institute in Opava
Winter 2013
Extent and Intensity
2/2/0. 6 credit(s). Type of Completion: z (credit).
Teacher(s)
doc. RNDr. Michal Marvan, CSc. (lecturer)
doc. RNDr. Michal Marvan, CSc. (seminar tutor)
Guaranteed by
doc. RNDr. Michal Marvan, CSc.
Mathematical Institute 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
there are 7 fields of study the course is directly associated with, display
Course objectives
Mathematical tools and methods of use in General Theory of Relativity.
Syllabus
  • Differentiable manifolds, smooth mappings, algebra of smooth functions.
    Tensor fields, tensor product, symmetries.
    Afinne connection, geodesics.
    Covariant derivative of tensor fields, torsion and curvature.
    Riemannian a pseudo-Riemannian structures, Levi-Civita connection.
    Lie derivative of tensor fields, Killing field.
Literature
    recommended literature
  • M. Kriele. Spacetime: Foundations of General Relativity and Differential Geometry. 1999. ISBN 978-3540663775. info
  • L. Krump, V. Souček, J. A. Tůšínský. Matematická analýza na varietách. Praha, Karolinum, 1998. info
  • O. Kowalski. Úvod do Riemannovy geometrie. Univerzita Karlova, Praha, 1995. info
  • S. W. Hawking, G. F. R. Ellis. The large scale structure of space-time. Cambridge University Press, 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
Oral examination.
The course is also listed under the following terms Winter 1999, Winter 2000, Winter 2001, Winter 2002, Winter 2003, Winter 2004, Winter 2005, Winter 2006, Winter 2007, Winter 2008, Winter 2009, Winter 2010, Winter 2011, Winter 2012, Winter 2014, Winter 2015, Winter 2016, Winter 2017, Winter 2018, Winter 2019.
  • Enrolment Statistics (Winter 2013, recent)
  • Permalink: https://is.slu.cz/course/sumu/winter2013/MU03256