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- Academic unit or major
- Mathematics
- Instructor(s)
- Yamada Sumio
- Class Format
- Lecture
- Media-enhanced courses
- Day/Period(Room No.)
- Intensive ()
- Group
- -
- Course number
- ZUA.E345
- Credits
- 2
- Academic year
- 2019
- Offered quarter
- 2Q
- Syllabus updated
- 2019/3/18
- Lecture notes updated
- -
- Language used
- English
- Access Index
-
Course description and aims
General Relativity is a subject where one aims to understand the geometric structure of spacetime, defined by a partial differential equation, called the Einstein equation. In this course, we aim to introduce some bacis topics related to the Einstein equation from the viewpoint of differential geometry. Given that it has been one hundred years since the discovery of the Einstein equation, and that the subject has grown immense since, we try to keep the background knowledge minimal, and the approach concise.
Student learning outcomes
One should master various methods to formulate the geometric structures of 4 dimensional spacetimes satisfying the Einstein equation, utilizing the languages of differential geometry as well as partial differential equations. Especially through investigating the geometric characteristics of the static and startionary solutions to the Einstein, equation, each student should grasp the importance of the Cauchy problem underlying the solution to the Einstein equation. With time permitting, one aims to understand the Hamiltonian formulation of the Einstein equation and its subsequent consequences fomulated by Penrose.
Keywords
Einstein equation, calculus of variations, Lorentzian geometry, Cauchy problem, Hamiltonian system
Competencies that will be developed
| ✔ Specialist skills | Intercultural skills | Communication skills | Critical thinking skills | Practical and/or problem-solving skills |
Class flow
This is a standard lecture course. There will be some assignments.
Course schedule/Required learning
| Course schedule | Required learning | |
|---|---|---|
| Class 1 | Minkowski spacetime and Maxwell equation Maxwell Equation as a Cauchy problem Levi-Civita connection and geodesics Derivation of the Einstein eqaution Post-Newtonian approximation Einstein equation as a Cauchy problem Geometry of Schwarzschild spacetime Positive mass theorem and Penrose inequality | Exercises will be presented during the lectures, and the collection of the exercises should constitute a report. |
Textbook(s)
None required
Reference books, course materials, etc.
Noel Hicks, Notes on Differential Geometry Robert Wald, Introduction to General Relativity P.Dirac, General Relativity 佐々木節,一般相対論
Assessment criteria and methods
Assignments (100%).
Related courses
- None
Prerequisites (i.e., required knowledge, skills, courses, etc.)
None Required
