General Relativity
Spacetime, geometry, and gravity explained step by step
General Relativity
Spacetime, explained step by step
Build the geometry first, then use it to understand gravity, black holes, gravitational waves, and the expanding universe.
Contents
The route through GR
Chapters will be added in this order.
3 chapters
Foundations
Build the mathematical and physical language needed for curved spacetime.
Spacetime
Describe events, intervals, light cones, and causality.
Coming soonVectors and tensors
Learn the objects that make physical laws coordinate-independent.
Coming soonCurves and motion
Move from ordinary trajectories to geometric paths through spacetime.
Coming soon3 chapters
Differential geometry
Turn curved spaces into a precise language for physics.
Manifolds
Describe spaces locally with coordinates and globally with charts.
Coming soonMetrics
Measure distances, times, angles, and causal structure geometrically.
Coming soonConnections and curvature
Compare vectors at different points and measure geometric bending.
Coming soon3 chapters
General relativity
Build Einstein’s theory from the equivalence principle and an action.
The equivalence principle
Understand why gravity can be described as spacetime geometry.
Coming soonEinstein equations
Relate spacetime curvature to matter and energy.
Coming soonGeodesics
Derive free fall as extremal motion in curved spacetime.
Coming soon3 chapters
Spacetime solutions
Explore the geometries that describe stars, black holes, and the universe.
Schwarzschild spacetime
Study the geometry outside a spherical, non-rotating body.
Coming soonBlack holes
Understand horizons, singularities, and causal structure.
Coming soonCosmology
Apply Einstein’s equations to an expanding homogeneous universe.
Coming soon3 chapters
Gravitational phenomena
Connect the geometry to observable effects and experiments.
Gravitational waves
Describe propagating distortions of spacetime and their detection.
Coming soonLensing and redshift
Calculate how gravity bends light and changes observed frequencies.
Coming soonTests of relativity
Compare geometric predictions with measurements in the solar system.
Coming soon