“Any fool can know. The point is to understand.”
― Albert Einstein
About this course:
- Lecturer: PD Dr. B. Metsch
- Year: 2018
- Difficulty:
- Course page: eCampus
- Tutor: A. Joshi
- Literature:
A nice course on general relativity. Like the other courses with this professor, it was kept very mathematical and complete, however making use of differential geometry (that is prior knowledge in this field) in the least possible manner. If you liked working with tensors in classical electrodynamics, you will love this course. To understand the physical meaning behind the math is not always easy though.
Exercise 1:
Keywords: Coordinate Transformations, Minkowski Metric, Spherical Polar Coordinates, Field Strength Tensor, Covariant Derivative, Christoffel Symbols, Levi-Civita Theorem, Real Vector Space, Skew-symmetric covariant Tensor, Determinant, Skew-symmetric contravariant Tensorfield
- A Coordinate Transformation
- Calculating with Christoffel Symbols
- Determinant Identities
Exercise 2:
Keywords: Christoffel Symbols, Transformation, Tensorfields, Contravariant Tensorfield, Curvature Tensor, Metric, Riemann Tensor, Riemann curvature Tensor, Properties
- Transformation of the Christoffel Symbols
- Curvature Tensor
Exercise 3:
Keywords: Covariant Derivative, Riemann Tensor, Riemann curvature Tensor, Bianchi Identities, Differential Bianchi Identities, Tensorial Relation, Locally inertial Coordinate System, Christoffel Symbols
- Bianchi Identities
Exercise 4:
Keywords: Vector Field, Differential Equation, One-parameter Family, Diffeomorphisms, Metrical Tensor, Action, Einstein Tensor, Einstein’s Equations, Einstein Field Equations
- Diffeomorphisms and Vector Fields
Exercise 5:
Keywords: Spherical Coordinates, Metrical Tensor, Partial Derivatives, Christoffel Symbols, Metric, Ricci Tensor, Ricci curvature Tensor, Ricci Scalar, Scalar Curvature, Einstein Tensor
- Spherically Symmetric Solution of the Einstein Equations II
Exercise 6:
Keywords: Einstein Equations, Einstein Field Equations, Dense Stars, Equation of State, Energy Density, Pressure, Ideal Gas, Spin-1/2 Particles, Wave Function, Particles in a Box, Spinor, Ground State, Fermi Momentum, Particle Density
- Equation of State for an Ideal Fermi Gas of Spin-1/2 Particles
Exercise 7:
Keywords: Spherically Symmetric Solution of Einstein’s Equations, Energy Density, Radius of a Star, Free input Parameter, Differential Equation, Einstein’s Equations, Einstein Field Equations, Star’s Boundary
- Stars with constant Energy Density
Exercise 8:
Keywords: Schwarzschild Metric, Clouds comoving Coordinates, Schwarzschild Coordinates, Metric, Interior Dust Cloud Metric, Comoving Coordinates, Scale Function, Differential Equation, Schwarzschild Domain
- Matching the Dust Cloud to the exterior Schwarzschild Metric
Exercise 9:
Keywords: Comoving Coordinates, Metric, Coordinate Transformation, Unit Vector
- The Dust Cloud Metric on S³
Exercise 10:
Keywords: Geodesic Equation, Solutions, Metric
- Geodesics
Exercise 11:
Keywords: Robertson-Walker Metric, Fundamental Equations of Cosmology, Metric, Universe dominated by Radiation, Equation of State
- The Robertson-Walker Metric for a Universe dominated by Radiation
Exercise 12:
Keywords: –
- No Homework