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| Lecture 1- Summary: Special Theory of Relativity: Inertial Reference Frame; Principle of relativity; Speed of propagation of interaction; Signal, event, world line; Invariant interval; Timelike and Spacelike intervals; Causal Structure; Proper Time; Lorentz Transformations; Proper length; velocities. Lecture 2- Geometry and the Dynamics in the Minkowski Space 4-vectors, tensors, metrics and all of that, Dynamics, Langrangian,energy, momentum, velocity, acceleration, force Lecture 3- Introduction to the Curved Spaces: Curved Spaces, Fragments of differential geometry, world according to curvilinear coordinates Lecture 4- General Theory of Relativity I: Principle of Equivalence. Moving freely in the freely falling elevator. Gravity, Lorentz Frames, Affine connection and Christoffel symbols Geodesics. Along comes Newtonian gravity Principle of General Covariance. Covariant Differentiation. Geodesic Equation from covariance principle. Covariant divergence and conserved quantities Lecture 5- General Theory of Relativity II: Riemann Curvature Tensor, Second Covariant derivatives of scalars, vectors and tensors Symmetries of the Riemann Tensor, Bianchi Identities, Einstein Tensor, Einstein's Field Equations, Energy Momentum Tensor, Cosmological Constant Lecture 6- GTR Solutions: Static and Spherical, Swartzshild Geometry, Oppenheimer-Volkoff Equations Some wonders of GTR Lecture 7- Cosmological Equations: MathCode Cosmological Principle, Friedmann-Lemaitre-Robertson-Walker metric, Cosmological Time and Horizons Cosmological Equations Lecture 8- Solution of Cosmological Equations: Matter Dominated Universe Radiation Dominated Universe The Einstein Static Universe, De Sitter Universe Lecture 9- Physical Cosmology: Cosmological Parameters, Redshift, Distances in Cosmology, Distance Redshift Relationship The Universe Today, Some Cosmological Problems Lecture 10- Inflation: Accelerated expansion, Scalar Fields in Cosmology, Slow Roll Inflation Lecture 11- Definition of Dark Matter Missing mass observations Lecture 12- Thermal Relic Paradigm |
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| ©2012 From Dwarfs to the Black Holes • Misak Sargsian | Lorum • Ipsum • Dolor • Sic Amet • Consectetur |
