General relativity is Einstein's theory of gravity, completed in 1915, in which gravitational phenomena are described through the geometry of spacetime rather than by Newton's concept of gravity as a force acting across space. Matter, energy, momentum and stress influence the curvature of spacetime, while freely falling objects follow the natural paths of that curved geometry called geodesics. The theory incorporates the principles of special relativity locally while extending them to situations involving gravity and arbitrary coordinate systems.
The central field equation relates the Einstein curvature tensor, the metric and the stress energy tensor, with a possible cosmological constant term. General relativity explains phenomena that Newtonian gravity cannot fully account for, including gravitational time dilation, the precise anomalous precession of Mercury's orbit, gravitational deflection of light, gravitational lensing, black holes, gravitational waves and the relativistic dynamics of the expanding universe.
A foundational idea behind general relativity is the equivalence principle. In its simplest form, the equivalence principle states that locally the effects of a uniform gravitational field are indistinguishable from the effects of uniform acceleration. An observer inside a freely falling lift experiences weightlessness because the observer and the lift are falling together. Conversely, an observer in an accelerating spacecraft can experience apparent gravity because the spacecraft accelerates relative to freely falling objects.
Einstein used this conceptual connection to recognise that gravity is fundamentally different from ordinary forces such as electromagnetism. A sufficiently small freely falling laboratory behaves approximately like an inertial frame of special relativity. The qualification locally is important because tidal gravitational effects cannot be eliminated over a sufficiently large region. Tidal effects arise because spacetime curvature causes nearby freely falling worldlines to converge or diverge differently. These tidal effects provide a physical manifestation of curvature rather than merely an artefact of coordinate choice.
General relativity represents spacetime using a metric tensor that determines distances, times and causal relationships between events. The metric is not simply a fixed background stage. It is a dynamical field influenced by the distribution of matter and energy. The Einstein field equations can be written schematically as G plus Lambda g equals 8 pi G divided by c to the fourth times T.
The Einstein tensor describes spacetime curvature, the metric tensor describes the geometry used to measure intervals, Lambda represents the cosmological constant, and T describes the stress energy content. The equation is highly nonlinear, meaning that gravitational fields can interact with themselves through the geometry. Solving it exactly is difficult and often requires symmetry assumptions or numerical computation. The Schwarzschild solution describes the exterior gravitational field of a nonrotating spherical mass, while the Kerr solution describes a rotating black hole. Other solutions describe cosmological expansion, gravitational waves and many more physical situations.
The Newtonian limit illustrates how general relativity contains classical gravity as an approximation. When gravitational fields are weak, velocities are much smaller than c and changes in the gravitational field are sufficiently slow, the equations reduce approximately to Newtonian gravitational behaviour. In this limit, the gravitational potential can be related to a component of the spacetime metric, and freely falling bodies follow trajectories that closely match Newton's equations.
This correspondence is important because general relativity did not simply discard centuries of successful mechanics. Instead, it explained why Newtonian gravity works so well under ordinary conditions and identified where it requires correction. Mercury's perihelion precession was an early important test because Newtonian planetary perturbations could not completely account for the observed excess. General relativity predicted the remaining contribution through the curvature of spacetime near the Sun, providing a quantitative success of the theory.
General relativity predicts that clocks run at different rates depending on gravitational potential. A clock deeper in a gravitational field is measured by a distant observer to run more slowly than a clock higher in the gravitational field, with the precise relationship determined by the spacetime geometry. This gravitational time dilation is distinct from the kinematic time dilation of special relativity, although both are manifestations of relativistic spacetime structure.
Gravitational redshift follows from the same principle: light climbing out of a gravitational field is observed at a lower frequency by a sufficiently distant observer. Precision experiments have measured gravitational redshift, including comparisons between clocks at different elevations. Satellite navigation systems must account for gravitational and velocity related clock differences simultaneously. The effect becomes extreme near compact objects such as neutron stars and black holes, where strong gravitational fields produce large differences in clock rates between different observers.
One of the most dramatic predictions of general relativity is the existence of black holes. A black hole forms when matter becomes sufficiently compact that an event horizon develops, creating a boundary beyond which signals cannot escape to distant observers through ordinary future directed causal paths. The Schwarzschild radius for a nonrotating uncharged mass M is 2GM divided by c squared. The event horizon is not a physical solid surface.
An observer freely falling through the horizon of a sufficiently massive black hole may not experience a locally dramatic event exactly at the horizon, although tidal forces can become enormous closer to the singularity depending on the black hole's mass and circumstances. The classical theory predicts singularities under broad conditions, where curvature becomes mathematically divergent or the classical spacetime description becomes incomplete. This is widely interpreted as evidence that general relativity alone is insufficient in such extreme regimes and must eventually be supplemented by quantum gravitational physics.
General relativity also predicts gravitational waves, which are propagating disturbances in spacetime geometry generated by accelerating asymmetric mass distributions, with especially strong signals produced by compact binary systems. The first direct detection of gravitational waves was made in 2015 by the Laser Interferometer Gravitational Wave Observatory, with the announcement occurring in 2016. The observed signal originated from the merger of two black holes and matched general relativistic predictions closely.
Gravitational wave astronomy has since become a new observational field capable of studying objects and events that may be difficult to observe through electromagnetic radiation. General relativity also predicts gravitational lensing, in which light follows curved null geodesics through curved spacetime and can be deflected by massive objects. Lensing can create multiple images, arcs and magnification and has become an important tool for studying galaxies, galaxy clusters and the distribution of matter, including dark matter.
General relativity forms the foundation of relativistic cosmology. Applying Einstein's equations to a homogeneous and isotropic universe produces the Friedmann equations, which describe how the scale factor of the universe evolves. These equations allow cosmological expansion to be related to the densities of matter, radiation and other components, together with spatial curvature and the cosmological constant. Modern cosmology uses general relativity to describe the large scale expansion of the universe and the dynamics of gravitational structure formation.
At the same time, general relativity has recognised limits. It is a classical theory and does not incorporate quantum mechanics in a complete way. Near the Planck scale, at extremely high curvatures and in theoretical descriptions of singularities, quantum gravitational effects are expected to become important. Candidate approaches include string theory, loop quantum gravity and other research programmes, but no experimentally established complete quantum theory of gravity has replaced general relativity. Its current status is therefore both extraordinarily successful and theoretically incomplete at the deepest fundamental level.
