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General relativity and cosmology course
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Module 3
The Principles of General Relativity
1
Minkowski Spacetime and Special Relativity
Formulate Special Relativity in the language of Minkowski spacetime as a manifold.
2
The Equivalence Principle and its Consequences
State the Principle of Equivalence and derive its immediate consequences, such as gravitational time dilation.
3
Stress-Energy Tensor for Fluids and Fields
Define the stress-energy tensor and construct it for a perfect fluid and the electromagnetic field.
4
Covariant Conservation of the Stress-Energy Tensor
Derive the covariant conservation law of the stress-energy tensor (∇μ Tμν = 0).
5
Einstein-Hilbert Action and EFE Derivation
Formulate the Einstein-Hilbert action and derive the Einstein Field Equations (EFE) via the variational principle.
6
Deriving the Einstein Constant from the Newtonian Limit
Analyze the Newtonian limit of the EFE to fix the value of the coupling constant κ.
7
The Initial Value Problem in General Relativity
Formulate the initial value problem of General Relativity using a spacelike hypersurface.
8
Killing Vectors, Spacetime Symmetries, and Noether's Theorem
Define Killing vector fields and their connection to spacetime symmetries and conserved quantities via Noether's theorem.
Previous module
Mathematical Foundations II: Curvature and Dynamics
Next module
Schwarzschild Black Holes and Classic Tests of GR