General Theory of Relativity
Gravity is not a force pulling across space. It is the shape of spacetime telling matter how to move.
Begin with the elevator↓The Equivalence Principle
Inside a sealed room, uniform acceleration feels locally identical to a uniform gravitational field.
Einstein’s elevator turns this observation into a rule: free fall removes the felt effects of gravity, while acceleration can create them. Over a small enough region, an observer cannot distinguish the two by a local experiment.
A / Standing in gravity
B / Accelerating upward
Spacetime Curvature
Mass and energy change the geometry of four-dimensional spacetime.
The familiar “rubber sheet” picture is only an analogy, but it captures one useful idea: the geometry around matter is not flat. Distances, directions, and elapsed time all depend on that curved geometry.
Following Geodesics
A freely falling object follows the straightest possible path through curved spacetime: a geodesic.
Planets orbit because their natural paths curve around the Sun’s distorted spacetime. They are continuously falling, not being tugged along a fixed track. Light follows null geodesics, so gravity can bend its path too.
Einstein’s Field Equations
The equations connect the contents of spacetime with the geometry of spacetime.
The left side describes curvature. The right side describes mass, energy, momentum, and pressure. Solutions to this relationship predict how spacetime behaves around stars, black holes, expanding universes, and moving masses.
Gravitational Time Dilation
A clock deeper in a gravitational field runs more slowly relative to a clock farther away.
There is no single universal clock. Each observer measures proper time along a path through spacetime. The difference is tiny near Earth, but measurable—and satellite navigation systems must account for it.
Black Holes & Event Horizons
A black hole forms when spacetime is curved so strongly that a boundary appears beyond which no outward path reaches the exterior.
That boundary is the event horizon. It is not a solid surface; it is a causal boundary. Once crossed, every future-directed path points farther inward. The glowing ring in the model represents hot material outside the horizon.
Gravitational Waves
Accelerating masses can create ripples in spacetime that travel outward at the speed of light.
Compact binaries—such as orbiting black holes or neutron stars—produce changing curvature. Passing waves alternately stretch and squeeze distances by an extraordinarily small amount. Their direct detection confirmed a major prediction of General Relativity.