Coordinate Transformations, Connection, and Pseudo-Riemannian Manifolds - Lecture 6

Explore advanced concepts in general relativity through this graduate-level lecture from the Warsaw4PhD and GeoPlanet PhD schools. Delve into relativistic velocity addition, time dilation formulas, and coordinate transformations. Examine Rindler's accelerating frame and uniformly rotating coordinates. Learn about differentiating vectors and tensors, and gain insights into pseudo-Riemannian manifolds. Presented by Mikołaj Korzyński from the Center for Theoretical Physics, Polish Academy of Sciences, this comprehensive lecture offers a deep dive into the mathematical foundations of spacetime and gravity.

00:00- Relativistic velocity addition
08:40- Time dilation formula
17:20- Coordinate transformations
26:43- Rindler’s accelerating frame
57:54- Break
58:10- Uniformly rotating coordinates
01:07:06- Differentiating vectors and tensors
01:29:52- Pseudo-Riemannian manifolds