Course Code ΤΑΕ452
Semester 8
Category Optional
Points 3
ECTS Units 6
Recommended Reading

J.L. Martin, Γενική Σχετικότητα, μια βασική εισαγωγή για φυσικούς, 2005, ΠΕΚ.

Bernard F. Schutz, A first course in General Relativity, 1985, Cambridge University Press.

Charles W. Misner, Kip S. Thorne and Hohn Archibald Wheeler, Gravitation, 1973, W.H. Freeman and Company.

L.D. Landau and E.M. Lifsitz, The classical theory of fields, 1970, Pergamon press.

Δ. Χατζηδημητρίου και Γ.Δ. Μπόζη, Εισαγωγή στην Μηχανική των Συνεχών Μέσων,  1997,  εκδόσεις Τζίολας.

Bernard F. Schutz, Geometrical methods of Mathematical Physics, 1980, Cambridge University Press.

Course Description
  1. REVIEW OF SPECIAL RELATIVITY Axioms. Lorentz transformations. Four-vectors. Spacetime (Minkowski) diagrams. Review of most important results.
  2. TENSOR ANALYSIS. Mathematical formalism. Applications in Special Relativity
  3. PERFECT FLUIDS. Perfect fluids in Special Relativity. Number Flux vector and Stress-Energy tensor.
  4. CURVED SPACETIME An overview of Differential Geometry.Covariant derivative. Parallel transport. Geodesics. Riemannian geometry. Bianchi identities: Ricci and Einstein tensors.
  5. GEOMETRIC THEORY OF GRAVITY Equivalence Principle and laws of physics in curved spacetime. Einstein’s field equations.
  6. GRAVITATIONAL RADIATION Generation, propagation and detection of Gravitation waves.
  7. RELATIVISTIC STARS Spherical stars. Pulsars, Neutron stars, Quasars and supermassive stars.
  8. GRAVITATIONAL COLLAPSE AND BLACK HOLES Schwarzschild geometry. Gravitational collapse Horizons and singularity theorems. Black holes.
  9. COSMOLOGY General relativistic cosmological models. Cosmological observations.