Course description

• Lecturer: Dr. Péter Lévay
• Time and place of lectures: Wednesday 10:15–12:00, room F3M01

Course requirements

• Students are given homework during lectures. These are simple exercises related to the given topic. 
• The condition of admittance to the exam and subscription is the submission of at least half of these homeworks.

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.

Relativity problem sets

relat1.pdf

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