Course data Course name: Theory of Relativity Neptun ID: BMETE15AF55 Responsible teacher: Péter Lévay Programme: BSc Physics Course data sheet: BMETE15AF55 Requirements, Informations 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