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General relativity and cosmology course
·
Module 10
Advanced Topics in Gravity
1
3+1 ADM Decomposition of Spacetime
Perform the 3+1 ADM decomposition of spacetime into space and time (lapse, shift, and spatial metric).
2
Extrinsic Curvature of a Spatial Slice
Derive the extrinsic curvature of the spatial slice.
3
Hamiltonian Formulation of General Relativity
Derive the Hamiltonian and momentum constraint equations of General Relativity.
4
The Wheeler-DeWitt Equation: A Quantum Gravity Candidate
Formulate the Wheeler-DeWitt equation as a candidate for a quantum theory of gravity.
5
Loop Quantum Gravity: Spin Networks, Area, and Volume
Introduce the basics of Loop Quantum Gravity: spin networks and the quantization of area and volume.
6
String Theory: Beyond Point Particles
Provide a conceptual overview of String Theory, including extra dimensions and the role of strings as fundamental objects.
7
Holography and AdS/CFT Correspondence
Discuss the AdS/CFT correspondence as a concrete realization of the holographic principle.
8
Modified Gravity as an Alternative to Dark Energy
Explore a class of modified gravity theories (e.g., f(R) gravity) as an alternative to dark energy.
End of course,
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