Course: Mathematical Foundations of the General Theory of Relativity I

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Course title Mathematical Foundations of the General Theory of Relativity I
Course code MU/03256
Organizational form of instruction Lecture + Lesson
Level of course Master
Year of study not specified
Semester Winter
Number of ECTS credits 6
Language of instruction Czech
Status of course Compulsory-optional
Form of instruction Face-to-face
Work placements This is not an internship
Recommended optional programme components None
Course availability The course is available to visiting students
Lecturer(s)
  • SERGYEYEV Artur, doc. RNDr. Ph.D.
  • NOVÁK Pavel, Mgr.
  • STOLÍN Oldřich, RNDr. Ph.D.
Course content
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.

Learning activities and teaching methods
unspecified
Recommended literature
  • L. Krump, V. Souček, J. A. Tůšínský. Matematická analýza na varietách. Praha, Karolinum, 1998.
  • M. Kriele. Spacetime: Foundations of General Relativity and Differential Geometry. 1999. ISBN 978-3540663775.
  • O. Kowalski. Úvod do Riemannovy geometrie. Univerzita Karlova, Praha, 1995.
  • S. W. Hawking, G. F. R. Ellis. The large scale structure of space-time. Cambridge University Press, 1973.


Study plans that include the course
Faculty Study plan (Version) Branch of study Category Recommended year of study Recommended semester
Mathematical Institute in Opava Geometry and Global Analysis (1) Mathematics courses 1 Winter
Faculty of Philosophy and Science in Opava Theoretical Physics (2) Physics courses - Winter
Mathematical Institute in Opava Mathematical Analysis (1) Mathematics courses 1 Winter
Mathematical Institute in Opava Mathematical Analysis (1-IVT) Mathematics courses 4 Winter