Course description:
Time and place of lectures: Wednesday 10:15–12:00, room F31SEM
Course requirements:
One of the conditions for signature: attending at least 70% of lectures.
Moreover, students will be given problem sets at the beginning of the lectures.
These are simple exercises related to the topic of the lecture.
The other condition of fulfilling the course is: presenting solutions to at least 70%
of these problems.
The solution of the problems will be evaluated with points 1- 5 that can be regarded as marks.
The solutions have to be presented in a weeks time. (Except for the first lecture when this is two weeks.)
There is no way to submit missed homework later.
The mark will be determined by the average of these points.
Some extra points might be earned by solving bonus problems.
The evaluation will be as follows:
0-40% fail (1)
41-55% pass (2)
56-70% average (3)
71-85% good (4)
80-100% excellent (5)
Topics:
Minkowski spacetime, four-vectors. Lorentz and Poincaré group.
Time dilation, length contraction, relativity of simultaneity. Velocity-addition formula, rapidity.
Causality, Zeeman theorem.
Proper time, four-velocity, four-acceleration.
Hyperbolic motion Relativistic dynamics.
Equivalence principle.
Equality of inertial and gravitational mass.
Principle of covariance.
Geodesic hypothesis, local inertial frames of reference.
Riemannian and Pseudo-Riemannian geometry, Christoffel symbols, geodesics.
Covariant derivative, parallel transport.
Newtonian limit, relationship of the metric tensor and the gravitational potential.
Derivation of the geodesic equation from the variational principle.
Riemann curvature tensor and its properties.
Riemann tensor and parallel transport along a closed curve.
The geodesic deviation equation.
Ricci tensor, scalar curvature, Bianchi identity, Einstein tensor. Stress-energy tensor, continuity equation, conservation laws.
Einstein equations, Einstein-Hilbert action.
Cosmological term.
Schwarzschild solution.
Perihelion precession of Mercury.
Suggested reading:
Gregory L. Naber: The Geometry of Minkowski Space Time
Stephen Weinberg: Gravitation and Cosmology: Principles and Applications of the General theory of Relativity
Robert M. Wald: General Relativity
https://edu.ttk.bme.hu/pluginfile.php/326/course/summary/relat1.pdf
- Tanár: Lévay Péter Pál