BMETE15AF46

Course data
Course name: Theory of Relativity
Neptun ID: BMETE15AF46
Responsible teacher: Péter Lévay
Department: Department of Theoretical Physics
Programme: BSc Physics
Course data sheet: BMETE15AF46
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