FYSS7320 General Relativity (9 cr)

Study level:
Advanced studies
Grading scale:
0-5
Language:
English, Finnish
Responsible organisation:
Department of Physics
Curriculum periods:
2020-2021, 2021-2022, 2022-2023

Description

  • Special relativity and differential geometry in the flat spacetime

  • Differential geometry in curved spacetimes

  • Covariant derivative, parallel transport, geodesics, Riemann tensor

  • Einstein equations, Newtonian limit, action of general relativity

  • Schwarzschild solution: dynamics, applications

  • Schwarzschild black hole: event horizon, causal structure, coordinate transformations, maximally extended solution

  • Gravitational waves: linear perturbations around the Minkowski spacetime, equation of motion for gravitational waves, impacts on test masses, sources of gravitational waves  

Learning outcomes

After the course the student should be able to:

  • Explain the basic features of the special and general relativity and their differences.

  • Compute the transformation of tensor components under coordinate transformations, take covariant derivatives of tensors, compute distances in the space-time and compute the connection coefficients and components of the Riemann tensor.

  • Determine the geodesic equations, explain their meaning and solve them in specific cases.

  • Explain the structure and contents of the Einstein equations, derive them by varying the action.

  • Write down the solution for the Schwarzschild spacetime, compute trajectories of test particles and gravitational redshifts in it.

  • Write down the metric for a Schwarzschild black hole inside the event horizon, form the maximally extended solutio and explain its causal structure.

  • Derive equations of motion for gravitational waves around the Minkowski solution, investigate how gravitational waves distort mutual distances of test masses, and compute the gravitational wave signal of a circular binary star system.  

Description of prerequisites

FYSA2002 Modern Physics, part B (special general relativity might be useful)

Study materials

WWW material and course book

Literature

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

Completion methods

Method 1

Description:
Given every other year.
Evaluation criteria:
Exercises and exam.
Time of teaching:
Period 3, Period 4
Select all marked parts

Method 2

Description:
This completion method is intended for students for whom method 1 is not possible for specific reasons (e.g. language, living elsewhere). Contact the teacher before enrolling to the course via this completion method.
Evaluation criteria:
Exam
Select all marked parts
Parts of the completion methods
x

Teaching (9 cr)

Type:
Participation in teaching
Grading scale:
0-5
Evaluation criteria:
Exercises and exam.
Language:
English, Finnish
Study methods:

Lectures, exercises, examination. 

Teaching

x

Independent study (9 cr)

Type:
Independent study
Grading scale:
0-5
Evaluation criteria:
Exam
Language:
English, Finnish
Study methods:

Self-study and exam. 

Teaching