Program Overview

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Course Information

Course Description

The course SH2374 General Relativity is a 7.5 credit course that covers the basics of differential geometry and the general theory of relativity. The course includes topics such as manifolds, covariant and contravariant vectors and tensors, transformation properties of tensors, and the Schwarzschild solution to Einstein's field equations.

Course Contents

• Basic differential geometry:
  • Manifolds
  • Local coordinates on manifolds
  • Covariant and contravariant vectors and tensors
  • Transformation properties of tensors
  • Vector fields
  • (Pseudo)-Riemannian metric
  • Covariant derivatives (Christoffel symbols and Levi-Civita connection)
  • Parallel transport and geodesics
  • Curved spaces
  • Lie derivatives and Killing vector fields
• General theory of relativity:
  • Basic concepts and principles in general relativity
  • Rindler coordinates
  • The Schwarzschild solution
  • Eddington–Finkelstein coordinates
  • Kruskal–Szekeres coordinates
  • Einstein's field equations
  • The Einstein–Hilbert action
  • The energy-momentum tensor
  • The weak field approximation
  • 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 passing the course, the student should be able to:

• Use differential geometry to describe the properties of a curved space and compute basic quantities in differential geometry
• Explain and interpret transformation properties of tensors
• Use the Schwarzschild solution to Einstein's field equations in vacuum and explain and interpret it in different coordinates
• Derive and use Einstein's field equations and describe the definition and role of the energy-momentum tensor in those
• Explain the physical interpretation of the components of the energy-momentum tensor and prove that Newton's theory of gravity is recovered in the non-relativistic limit
• Calculate physical quantities for test particles in a given solution to Einstein's field equations
• Describe 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 evolves in time
• Describe the ideas behind cosmological inflation and dark energy

Literature and Preparations

Specific Prerequisites

• English B/English 6
• SH2373 Special Relativity and good knowledge of multivariable calculus
  • Note: SH2373 can be studied in parallel

Literature

Information about course literature can be found 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 - Examination, 7.5 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

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

Further Information

Course Room in Canvas

Registered students find further information about the implementation of the course in the course room in Canvas

Offered by

SCI/Physics

Main Field of Study

Engineering Physics

Education Cycle

Second cycle

Information per Course Offering

Termin

Spring 2026

Information for Spring 2026 Start 16 Mar 2026 Programme Students

• Course location: AlbaNova
• Duration: 16 Mar 2026 – 1 Jun 2026
• Periods: Spring 2026: P4 (7.5 hp)
• Pace of study: 50%
• Application code: 61092
• Form of study: Normal Daytime
• Language of instruction: English
• Course memo: Course memo is not published
• Number of places: Places are not limited
• Target group: No information inserted
• Planned modular schedule: No information inserted
• Schedule: Link to schedule
• Part of programme:
  • Master's Programme, Engineering Physics, year 1, TFYA
  • Master's Programme, Engineering Physics, year 1, TFYB

Contact

• Examiner: Tommy Ohlsson
• Course coordinator: Tommy Ohlsson
• Teachers:
  • Matthias Flór
  • Tommy Ohlsson