Academic Team
Content Course
Type: Optional– PEC&AC Track – 3rd Trimester
This course covers advanced mathematical and theoretical tools for modern gravitational physics. It combines in-depth study of differential geometry, Hamiltonian formulations of General Relativity, and black hole thermodynamics, with an introduction to extensions of Einstein’s theory.
Main Topics
- Advanced differential geometry: differential forms, Lie groups and algebras, Yang–Mills fields, spinors in curved space, first-order formalism of General Relativity, and elements of supergravity.
- Hamiltonian formalism of GR: ADM mass, time, and conserved quantities.
- Conserved charges in gauge and gravitational theories: Komar integrals, Abbott–Deser approach, Witten’s positive mass theorem.
- Black hole thermodynamics: laws of black hole mechanics, cosmic censorship, singularity theorems, horizon topology, and no-hair results.
- Extensions of GR: scalar–tensor theories, f(R)f(R)f(R) gravity, Lovelock theories, topological terms, and 3D gravity.
Reading List
- Spacetime and Geometry, Carroll, Cambridge University Press (2019)
- Gravitation; Misner, Thorne, Wheeler, and Freeman (1970)
- General Relativity; Wald, The University Chicago Press (1984)
- Gravitation and Cosmology; Weinberg, Addison Wesley (1978)
- Gravity: Newtonian, Post Newtonian, Relativistic; Poisson and Will, Cambridge University Press (2014)
- The large scale structure of spacetime; Hawking and Ellis, Cambridge University Press (1973)
Teaching Plan Information
Course Schedule
