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SH2372 General Relativity

Course Description

The course covers the basics in general relativity and goes through the underlying mathematical framework, the physical interpretations, as well as the simplest space-time solutions with applications in, for example, cosmology.

Information per Course Offering

Course Syllabus

The course syllabus is available as a PDF. Please note that all information from the Course syllabus is available on this page in an accessible format.

Content and Learning Outcomes

Course Contents

• Basic differential geometry: Local coordinates on manifolds. Covariant and contravariant vector and tensor fields. (Pseudo-) Riemann metric. Covariant differentiation (Christoffel symbols, Levi-Civita connection). Parallel transport. Curved spaces. Lie derivatives and Killing vector fields.
• General theory of relativity: Basic concepts in general relativity. Schwarzschild spacetime. Einstein's field equations. The energy-momentum tensor. Weak field limit. Experimental tests of general relativity. Gravitational lensing. Gravitational waves. Introductory cosmology (including the Friedmann–Lemaître–Robertson–Walker metric), including inflation and dark energy.

Intended Learning Outcomes

After completing the course, you should be able to:

• Use differential geometry to describe the properties of a curved space and compute basic quantities in differential geometry.
• Derive and use Einstein's field equations and describe the definition and role of the energy-momentum tensor in those, account for the physical interpretation of its components, and prove that Newton's theory of gravity is recovered in the non-relativistic limit.
• Compute physical quantities for test particles in a given solution to Einstein's field equations, e.g., particle trajectories and proper times.
• Give an account of the experiments with which the general theory of relativity has been tested and compare with predictions from Newton's theory of gravity.
• Use the Friedmann–Lemaître–Robertson–Walker metric to describe the different possibilities for how a homogeneous universe develops with time as well as describe the ideas behind cosmological inflation and dark energy.

Literature and Preparations

Specific Prerequisites

• SI2371 Special relativity and good knowledge of multivariable differential calculus. SI2371 may be studied in parallel.
• English B / English 6

Literature

You can find information about course literature either in the course memo for the course offering or in the course room in Canvas.

Examination and Completion

Grading Scale

• A, B, C, D, E, FX, F

Examination

• TEN1 - Written exam, 6.0 credits, grading scale: A, B, C, D, E, FX, F

Based on recommendation from KTH's coordinator for disabilities, the examiner will decide how to adapt an examination for students with documented disability.

The examiner may apply another examination format when re-examining individual students.

If the course is discontinued, students may request to be examined during the following two academic years.

The course is examined through an exam, which normally is a written exam.

Further Information

Offered by

SCI/Physics

Main Field of Study

Engineering Physics

Education Cycle

Second cycle

Course Details

• Credits: 6.0
• Last planned examination: Autumn 2026
• Decision to discontinue this course: No information inserted
• Examiner: Tommy Ohlsson
• Ethical approach: All members of a group are responsible for the group's work. In any assessment, every student shall honestly disclose any help received and sources used. In an oral assessment, every student shall be able to present and answer questions about the entire assignment and solution.