General Relativity: Reopening the Lecture Archive

I am reopening my archive of general relativity lectures for Master’s students in theoretical physics.

The archive contains 54 videos in English and Arabic. Most recordings are from 2022, with earlier material from 2021 and 2020. The recordings vary in quality and presentation style. I had withdrawn them intending to produce improved versions—in language, scientific exposition, and visual presentation. Since I have not been able to carry out that project, I have decided to make the existing lectures available again, hoping they will remain useful to students.

The course follows six main stages:

1. Relativistic foundations: special relativity, the Minkowski metric, proper time, Lorentz transformations, and the equivalence principle.
2. Differential geometry: manifolds, vectors, geodesics, and tensors.
3. Curvature: parallel transport, covariant derivatives, connections, the Riemann curvature tensor, and geodesic deviation.
4. Einstein’s equations: Ricci curvature, the stress-energy-momentum tensor, perfect fluids, the Newtonian limit, and the derivation of Einstein’s equations from the Hilbert–Einstein action.
5. Exercises and further topics: the geometry of the two-sphere, the cosmological principle, maximally symmetric spaces, the Robertson–Walker metric, the ADM Hamiltonian formulation, and a review of differential geometry.
6. Supplementary cosmology and astrophysics: cosmic scales, flatness, topology, the size of the universe, and stellar ages and masses.

Many topics have alternative recordings in Arabic and English, but the pairing is not uniform. Some subjects have only one recording, while others are covered through several complementary lectures. In particular, the Arabic and English recordings numbered “Einstein’s equations 4” and “Einstein’s equations 5” cover related but different material.

Students need not watch every alternative recording of a given topic. They can choose the language and presentation that suit them, while consulting complementary recordings for additional material.

The downloadable table of contents includes the course outline and direct clickable links to all 54 videos.

Download the PDF table of contents:

https://drive.google.com/file/d/16OAE_Ieb4QcmE8K4vzbghvHowUk3Ocqa/view?usp=sharing

Watch the complete playlist:

https://www.youtube.com/playlist?list=PLsHtEvuFFjBsmCTY_lwlQK1cJe_VPAYSY