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Theory of Relativity, 6 credits
Relativitetsteori, 6 hp
TATA75
Main field of study
Mathematics Applied Mathematics Applied Physics PhysicsCourse level
Second cycleCourse type
Programme courseExaminer
Fredrik AnderssonDirector of studies or equivalent
Göran ForslingEducation components
Preliminary scheduled hours: 38 hRecommended self-study hours: 122 h
ECV = Elective / Compulsory / Voluntary
Main field of study
Mathematics, Applied Mathematics, Applied Physics, PhysicsCourse level
Second cycleAdvancement level
A1XCourse offered for
- Physics and Nanoscience, Master's Programme
- Applied Physics and Electrical Engineering - International, M Sc in Engineering
- Applied Physics and Electrical Engineering, M Sc in Engineering
Specific information
The course is only offered every second year. It will be offered during 2016.
Prerequisites
Mechanics, Modern Physics.In addition to these formal prerequisites considerable 'mathematical maturity' is required. Therefore it is advantageous to have taken one or several additional courses in advanced mathematics and theoretical physics e.g., Complex analysis, Differential geometry, Functional analysis, Cosmology and/or Analytical mechanics.
Intended learning outcomes
The purpose of the course is to give a good understanding of the principles and consequences of the special and general theory of relativity. After a finished course the student knows how to:
- use the relativistic introductory four formalism to solve problems within the special relativity
- use the mathematical formalism for connections and general tensors (like the Riemann tensor) to solve problems of general relativistic nature
- explain the physical principles that form the foundation for general relativity and derive their consequences for the field equations and equations of motion
- derive the physical consequences of general relativity from the field equations and equations of motion, especially the classical tests of the theory, black holes and relativistic cosmology
- derive the main exact solutions of Einsteins field equations
Course content
Manifolds. Tensor algebra. Tensor analysis. Metric tensor.
Geodesics. Riemann tensor. Calculus of variations. The postulates of special
relativity. Lorentz-transformations. Physical consequences of special relativity. The postulates of general relativity. Einstein's field equations and equations of motion. Weak-field approximation. Schwarzschild's solution. Planetary motion and the perihelion drift of Mercury. Deviation of light. Gravitational redshift. Time dilation. Singularities. Static and rotating black holes. Relativistic cosmology.
Teaching and working methods
The course is presented on lectures.
Examination
| UPG1 | Homework problems and oral presentation | 6 credits | U, 3, 4, 5 |
Grades
Four-grade scale, LiU, U, 3, 4, 5Department
Matematiska institutionenDirector of Studies or equivalent
Göran ForslingExaminer
Fredrik AnderssonCourse website and other links
http://www.mai.liu.se/und/kurser/index-amne-tm.htmlEducation components
Preliminary scheduled hours: 38 hRecommended self-study hours: 122 h
Course literature
FR D'Inverno: Introducing Einsteins Relativity, Clarendon| Code | Name | Scope | Grading scale |
|---|---|---|---|
| UPG1 | Homework problems and oral presentation | 6 credits | U, 3, 4, 5 |
Regulations (apply to LiU in its entirety)
The university is a government agency whose operations are regulated by legislation and ordinances, which include the Higher Education Act and the Higher Education Ordinance. In addition to legislation and ordinances, operations are subject to several policy documents. The Linköping University rule book collects currently valid decisions of a regulatory nature taken by the university board, the vice-chancellor and faculty/department boards.
LiU’s rule book for education at first-cycle and second-cycle levels is available at http://styrdokument.liu.se/Regelsamling/Innehall/Utbildning_pa_grund-_och_avancerad_niva.
Course literature is preliminary.
FR D'Inverno: Introducing Einsteins Relativity, Clarendon
Note: The course matrix might contain more information in Swedish.
I = Introduce, U = Teach, A = Utilize
| I | U | A | Modules | Comment | ||
|---|---|---|---|---|---|---|
| 1. DISCIPLINARY KNOWLEDGE AND REASONING | ||||||
| 1.1 Knowledge of underlying mathematics and science (G1X level) |
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X
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X
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UPG1
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| 1.2 Fundamental engineering knowledge (G1X level) |
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| 1.3 Further knowledge, methods, and tools in one or several subjects in engineering or natural science (G2X level) |
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| 1.4 Advanced knowledge, methods, and tools in one or several subjects in engineering or natural sciences (A1X level) |
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| 1.5 Insight into current research and development work |
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| 2. PERSONAL AND PROFESSIONAL SKILLS AND ATTRIBUTES | ||||||
| 2.1 Analytical reasoning and problem solving |
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X
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X
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UPG1
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| 2.2 Experimentation, investigation, and knowledge discovery |
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X
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| 2.3 System thinking |
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| 2.4 Attitudes, thought, and learning |
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X
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X
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UPG1
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| 2.5 Ethics, equity, and other responsibilities |
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| 3. INTERPERSONAL SKILLS: TEAMWORK AND COMMUNICATION | ||||||
| 3.1 Teamwork |
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| 3.2 Communications |
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X
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UPG1
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| 3.3 Communication in foreign languages |
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X
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| 4. CONCEIVING, DESIGNING, IMPLEMENTING AND OPERATING SYSTEMS IN THE ENTERPRISE, SOCIETAL AND ENVIRONMENTAL CONTEXT | ||||||
| 4.1 External, societal, and environmental context |
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| 4.2 Enterprise and business context |
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| 4.3 Conceiving, system engineering and management |
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| 4.4 Designing |
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| 4.5 Implementing |
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| 4.6 Operating |
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| 5. PLANNING, EXECUTION AND PRESENTATION OF RESEARCH DEVELOPMENT PROJECTS WITH RESPECT TO SCIENTIFIC AND SOCIETAL NEEDS AND REQUIREMENTS | ||||||
| 5.1 Societal conditions, including economic, social, and ecological aspects of sustainable development for knowledge development |
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| 5.2 Economic conditions for knowledge development |
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| 5.3 Identification of needs, structuring and planning of research or development projects |
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| 5.4 Execution of research or development projects |
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| 5.5 Presentation and evaluation of research or development projects |
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