Free online courseRelativity Course: Special and General Relativity, Tensors, Black Holes, Gravitational Waves and Cosmology

Course Description

Dive into the foundations of modern physics with this free online course on special and general relativity, designed to build real intuition alongside the mathematical tools used in contemporary theory. Starting from Galilean relativity, you will develop the language of spacetime diagrams, intervals, and transformation rules, then progress to the geometry and equations of Lorentz transformations, time dilation, length contraction, and relativistic dynamics with 4-vectors.

As the course advances, you will explore accelerated motion and its consequences through hyperbolic trajectories, horizons, and classic thought experiments, while learning how changing coordinates reshapes the way physics is expressed. You will also gain a practical understanding of covariance, contravariance, Jacobians, and covariant derivatives, forming a clear bridge from flat spacetime to curved geometry.

From there, the course moves into the core ideas of general relativity: equivalence, manifolds, geodesics, and curvature described through the Riemann and Ricci tensors and related scalars. You will connect gravity to spacetime structure via the stress-energy-momentum tensor and follow the logic leading to the Einstein field equations. With these foundations, you will investigate the Schwarzschild solution, interpret gravitational time dilation and horizons, and examine geodesic motion and coordinate extensions that clarify black hole physics and related spacetime features.

To round out the journey, you will study gravitational waves through linearized gravity, gauge choices, polarizations, and physical effects on free particles, linking theory to landmark detections. Finally, you will step into cosmology, developing the FLRW metric, redshift, horizons, comoving coordinates, and the Friedmann equations to understand expanding-universe models and the evolution of cosmic geometry.