MU:MU03256 General Relativity I - Course Information

MU03256 Mathematical Foundations of the General Theory of Relativity I

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

• Geometry and Global Analysis (programme MU, N1101)
• Mathematical Analysis (programme MU, M1101)
• Mathematical Analysis (programme MU, N1101)
• Theoretical Physics (programme FPF, M1701 Fyz)
• Theoretical Physics (programme FPF, N1701 Fyz)
• Secondary School Teacher Traning in Physics and Mathematics (programme FPF, M1701 Fyz)
• Secondary School Teacher Training in Mathematics (programme FPF, M7504)

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.

• Enrolment Statistics (Winter 2012, recent)
  
• Permalink: https://is.slu.cz/course/sumu/winter2012/MU03256