General relativity

is the curvature scalar. The Ricci tensor itself is related to the more general Riemann curvature tensor as

In general relativity, the world line of a particle free from all external, non-gravitational force is a particular type of geodesic in curved spacetime. In other words, a freely moving or falling particle always moves along a geodesic.

The derivation outlined in the previous section contains all the information needed to define general relativity, describe its key properties, and address a question of crucial importance in physics, namely how the theory can be used for model-building.

General relativity has a number of physical consequences. Some follow directly from the theory's axioms, whereas others have become clear only in the course of many years of research that followed Einstein's initial publication.

Schematic representation of the gravitational redshift of a light wave escaping from the surface of a massive body
Deflection of light (sent out from the location shown in blue) near a compact body (shown in gray)
Ring of test particles deformed by a passing (linearized, amplified for better visibility) gravitational wave

General relativity differs from classical mechanics in a number of predictions concerning orbiting bodies. It predicts an overall rotation (precession) of planetary orbits, as well as orbital decay caused by the emission of gravitational waves and effects related to the relativity of direction.

Newtonian (red) vs. Einsteinian orbit (blue) of a lone planet orbiting a star. The influence of other planets is ignored.
Simulation based on the equations of general relativity: a star collapsing to form a black hole while emitting gravitational waves
The ergosphere of a rotating black hole, which plays a key role when it comes to extracting energy from such a black hole
Observation of gravitational waves from binary black hole merger GW150914