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

Course Description

Relativity can feel like a collection of paradoxes and exotic claims until you learn to see it as a clean geometric framework. This free online physics course guides you from everyday reference frames to the modern picture of spacetime, helping you replace memorized slogans with clear reasoning. You will start with Galilean relativity and spacetime diagrams, then discover exactly why classical ideas break down when electromagnetism enters the story and why a new transformation is needed.

From there, special relativity becomes a set of powerful tools rather than a source of confusion. By connecting geometry with the Lorentz transformation, you will develop an intuitive understanding of time dilation, length contraction, relativity of simultaneity, velocity addition, and the spacetime interval. You will also learn to work with four-vectors and relativistic energy and momentum, tying the famous results to a consistent mathematical structure that you can actually use to solve problems.

Next, the course builds the bridge from accelerated motion to gravity. You will explore proper acceleration, horizons in accelerating frames, and classic thought experiments like the twin paradox and Bell’s spaceship paradox, with careful attention to what is measured, by whom, and why. Along the way, you will gain confidence with covariance, contravariance, Jacobians, and the role of metrics and covariant derivatives when coordinates are no longer inertial.

General relativity is introduced from first principles, emphasizing the equivalence principle, curved manifolds, and curvature described by tensors such as the Riemann and Ricci tensors. You will see how matter and energy are encoded by the stress-energy-momentum tensor and how the Einstein field equations connect geometry to physics. With that foundation, the course develops the Schwarzschild spacetime and uses it to explain gravitational time dilation, event horizons, orbits, and coordinate choices that reveal what is truly physical near a black hole.

Finally, you will connect theory to observation through gravitational waves and cosmology. By working in weak-field approximations and useful gauges, you will understand what detectors like LIGO measure and how waves influence distances. The course then turns to the expanding universe using the FLRW metric and the Friedmann equations, explaining redshift, horizons, cosmic rest frames, and the evidence for accelerated expansion. Exercises throughout reinforce each step so you can follow the full arc from spacetime diagrams to black holes and the evolution of the universe.