Academic Team
Course Content
Type: Compulsory– PEC&AC Track – 1stTrimester
This course offers an in-depth study of gravity as described by Einstein’s General Theory of Relativity. Students will explore gravity as a geometric property of spacetime, learn to derive and interpret exact solutions to Einstein’s equations, and understand their cosmological and astrophysical relevance.
Main Topics
- Foundations of General Relativity: equivalence principles, covariance, and differential geometry.
- Einstein’s field equations: vacuum and matter solutions, weak field limits, and exact metrics like Schwarzschild, Reissner-Nordström, and Kerr.
- Experimental tests of General Relativity and classical Solar System tests.
- Introduction to black hole physics, including singularities, event horizons, and black hole mechanics.
- Gravitational waves: theory, emission, and modern detection methods.
- Astrophysical applications: black hole mergers and supermassive black holes in galaxies.
Skills Acquired
- Understand gravity as a geometric effect on spacetime structure.
- Derive and analyze key exact solutions of Einstein’s equations.
- Relate theory with experimental and observational tests.
- Gain insight into current research topics like gravitational waves and black hole astrophysics.
Reading List
- Lecture Notes on General Relativity by Daniel Baumann (all sections except Section 7 on Cosmology).
Additional Recommended Books:
- Sean M. Carroll, Spacetime and Geometry
- James Hartle, Gravity
- Bernard Schutz, A First Course in Relativity
- Ray d’Inverno, Introducing Einstein’s Relativity
- M. P. Hobson et al., General Relativity
- Anthony Zee, Einstein Gravity in a Nutshell
- Robert M. Wald, General Relativity
- Steven Weinberg, Gravitation and Cosmology
- P. A. M. Dirac, General Theory of Relativity
- Misner, Thorne & Wheeler, Gravitation
- Eric Poisson & Clifford Will, Gravity
- Yvonne Choquey-Bruhat, Introduction to General Relativity
Course Outline:
- Special Relativity: Lorentz transformations, spacetime, relativistic kinematics and dynamics
- Gravity as Geometry: equivalence principle, curved spacetime
- Differential Geometry basics: manifolds, tensors, metric
- Geodesics: equations, Newtonian limit, applications (Mercury precession, light bending)
- Spacetime Curvature: covariant derivatives, Riemann tensor, geodesic deviation
- Einstein Equations: field equations, matter, cosmological constant, vacuum solutions
- Gravitational Waves: linearized gravity, wave creation
- Black Holes: Schwarzschild, charged, rotating
Teaching Plan Information
Course Schedule
