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MASS 2026 Course: Gravitation and Cosmology
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Lecture |
Presentation |
| Syllabus: course overview |
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pdf |
Part 1: General Relativity
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| 01. |
General Relativity as a geometric theory of gravitation, spacetime, manifolds,
scalars, vectors and dual vectors: contravariant and covariant transformation rules |
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pdf |
| 02. |
Tensors: transformation rules, metric (fundamental) tensor and tensor algebra
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pdf |
| 03. |
Reference frames, basics of Special Relativity, Minkowski spacetime, Lorentz
transformations, energy-momentum tensor and perfect fluid |
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pdf |
| 04. |
Basic principles of General Relativity: principle of equivalence and principle of
general covariance, locally inertial frame, affine connection, geodesic equation |
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pdf |
| 05. |
Covariant differentiation, parallel transport, minimal-coupling principle,
Riemann-Christoffel curvature tensor, Ricci tensor and scalar curvature |
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pdf |
| 06. |
Lagrangian, action, Hamilton's principle of least action, Einstein-Hilbert action,
matter action, calculus of variations, Einstein field equations |
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pdf |
| 07. |
Vacuum solutions: Schwarzschild, Kerr, Reissner-Nordström and Kerr-Newman
metric, classic Solar System tests of GR and Lense-Thirring effect |
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pdf |
| 08. |
Other experimental tests: black holes, single and binary supermassive black holes,
their shadows, relativistically broadened spectral lines and gravitational waves |
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pdf |
Part 2: Cosmology
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| 09. |
Cosmological principle, Friedmann-Lemaître-Robertson-Walker metric, Friedmann
equations, cosmological parameters, standard ΛCDM cosmological model |
zip |
pdf |
| 10. |
Distance measures in cosmology: proper and comoving distance, angular diameter
distance, luminosity distance, distance-duality relation |
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pdf |
| 11. |
Observational cosmology: determination of cosmological parameters using Type Ia
supernovae and cosmic microwave background radiation |
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pdf |
| 12. |
Gravitational lenses (basic principles, types and cosmological applications),
problems of the ΛCDM model: Hubble tension and cosmological constant problem |
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pdf |