FYSS7320 General Relativity (9 cr)

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Study level:

Advanced studies

Grading scale:

0-5

Language:

English, Finnish

Responsible organisation:

Department of Physics

Curriculum periods:

2017-2018, 2018-2019, 2019-2020

Description

Content

The course provides an introduction to General Relativity which is a classical theory of gravity. General Relativity describes gravity as curvature of the spacetime and it includes Newton’s gravity as the weak field limit. Topics included contain a brief review of special relativity, introduction to differential geometry and curved spacetimes, Einsteins equations and curvature, Schwartzschild solution for stars and black holes and gravitational waves if time allows. In particular, the course aims to provide the theoretical background and tools useful for lecture courses on cosmology.

Completion methods

Assignments, examination

Assessment details

The final grade is based on the examination (75 %) and assignments (25 %).

Learning outcomes

At the end of the course, students will be able to explain the basic concepts of special and general relativity and their differences. Students will be able to compute the transformation of tensor components under coordinate transformations and form covariant derivatives, compute distances between points of the spacetime using the metric as well as compute the connection coefficients and the curvature tensor from the metric. Students will be able to form the geodesics equations, understand their meaning and solve them in simple setups. Students will also be able to form Einstein equations by varying the action and understand their meaning as well as solve Einstein equations for a spherically symmetric, static, empty space outside a star (Scwartzschild) and compute orbits of test bodies and light and gravitational redshifts in the Schwartzschild space.

Additional information

Given on spring semester, every two years starting spring 2018.

Description of prerequisites

Students are expected to have knowledge of Mechanics (FYSP1010) and Modern Physics (FYSA2001-2002).

Literature

S.M. Carroll, Spacetime and Geometry (Addison Wesley 2004)

Completion methods

Method 1

Select all marked parts

Parts of the completion methods

Unpublished assessment item