MASS 2023 Course: Gravitation and Cosmology



Syllabus: course overview odp pdf

Part 1: General Relativity

01. General Relativity as a geometric theory of gravitation, spacetime, manifolds odp pdf
02. Vectors and tensors
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03. Metric (fundamental) tensor and tensor algebra
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04. Reference frames, basics of Special Relativity, Minkowski spacetime, Lorentz
transformations, energy-momentum tensor and perfect fluid
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05. Basic principles of General Relativity: principle of equivalence and principle of
general covariance, locally inertial frame, affine connection, geodesic equation
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06. Covariant differentiation, parallel transport, minimal-coupling principle,
Riemann-Christoffel curvature tensor, Ricci tensor and scalar curvature
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07. Calculus of variations, Lagrangian, action and principle of least action
(Hamilton's principle), Hilbert action, Einstein field equations
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08. Vacuum solutions: Schwarzschild, Kerr, Reissner-Nordström and Kerr-Newman
metric, black holes, classic Solar System and other experimental tests of GR
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Part 2: Cosmology

09. Cosmological principle, Friedmann-Lemaître-Robertson-Walker metric, Friedmann
equations, cosmological parameters, standard ΛCDM cosmological model
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10. Distance measures in cosmology: proper and comoving distance, angular diameter
distance, luminosity distance, distance-duality relation
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11. Observational cosmology: determination of cosmological parameters using Type Ia
supernovae and cosmic microwave background radiation
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12. Gravitational lenses (basic principles, types and cosmological applications),
problems of the ΛCDM model: Hubble tension and cosmological constant problem
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Exercises in Python