General relativity (GR) is a geometric theory of gravitation published by Albert Einstein in 1915. It supersedes Newton's law of universal gravitation for regimes involving strong gravitational fields, high velocities, or cosmological scales. The theory describes gravity not as a force acting at a distance but as a curvature of four-dimensional spacetime caused by the presence of mass and energy. General relativity is expressed mathematically through the Einstein field equations, a system of ten interrelated partial differential equations relating the geometry of spacetime (encoded in the Einstein tensor) to the distribution of matter and energy (encoded in the stress-energy tensor).

The core postulate of general relativity is the equivalence principle: locally, a freely falling frame of reference is indistinguishable from an inertial frame in the absence of gravity. This principle, combined with the requirement that the laws of physics take the same form in all reference frames (general covariance), motivates the description of gravity as spacetime curvature. The mathematical language of GR is differential geometry, specifically Riemannian geometry generalized to pseudo-Riemannian manifolds with Lorentzian signature.

The Einstein field equations are written compactly as:

G_μν + Λg_μν = (8πG/c⁴) T_μν

where G_μν is the Einstein tensor (encoding spacetime curvature), Λ is the cosmological constant, g_μν is the metric tensor, G is Newton's gravitational constant, c is the speed of light, and T_μν is the stress-energy tensor. The metric tensor is the central dynamical object: it encodes distances, angles, and the causal structure of spacetime, and its derivatives determine the curvature.

Exact solutions to the field equations exist for idealized configurations. The Schwarzschild solution describes the spacetime exterior to a spherically symmetric, non-rotating mass and predicts the existence of black holes - regions from which no causal influence can escape. The Kerr solution extends this to rotating masses. The Friedmann-Lemaître-Robertson-Walker (FLRW) metric describes a homogeneous, isotropic expanding universe and forms the mathematical basis of modern cosmology.

General relativity makes several predictions that differ from Newtonian gravity and have been confirmed observationally:

• Perihelion precession - GR correctly accounts for the anomalous precession of Mercury's perihelion (approximately 43 arcseconds per century beyond Newtonian predictions), which had been unexplained since the mid-19th century.
• Gravitational deflection of light - Starlight passing near the Sun is deflected by approximately 1.75 arcseconds, twice the Newtonian prediction. This was confirmed during the solar eclipse of 29 May 1919 by expeditions led by Arthur Eddington.
• Gravitational redshift - Photons lose energy climbing out of a gravitational well, shifting their frequency toward the red. This was confirmed in the Pound-Rebka experiment (1959) and is a practical consideration in GPS satellite clock corrections.
• Gravitational time dilation - Clocks run slower in stronger gravitational fields, a prediction confirmed by atomic clock experiments at different altitudes.
• Gravitational waves - GR predicts that accelerating masses radiate gravitational waves - ripples in spacetime curvature propagating at the speed of light. Indirect evidence came from the orbital decay of the Hulse-Taylor binary pulsar (1974). Direct detection was achieved by the LIGO collaboration on 14 September 2015, observing a signal consistent with the merger of two stellar-mass black holes. ¹⁾
• Geodetic and frame-dragging precession - Confirmed by Gravity Probe B (results published 2011) to within experimental uncertainty.
• Shapiro delay - Radar signals passing near the Sun arrive later than predicted by Newtonian geometry, consistent with GR.
• Black hole imaging - The Event Horizon Telescope collaboration released the first resolved image of the shadow of the supermassive black hole in M87 in 2019, and of Sagittarius A* (the Milky Way's central black hole) in 2022, consistent with Kerr metric predictions.

General relativity is a classical field theory and is not compatible, as currently formulated, with quantum mechanics. At the Planck scale (approximately 10⁻³⁵ meters and 10⁻⁴³ seconds), quantum effects are expected to become relevant to spacetime structure, but no empirically confirmed theory of quantum gravity exists. Candidate frameworks include loop quantum gravity, string theory, and causal dynamical triangulations, among others. The incompatibility between GR and the Standard Model of particle physics is one of the central unsolved problems in theoretical physics. See Quantum Gravity - Debate and Quantum Gravity for further discussion.

The FLRW solution, combined with observational data, supports the standard cosmological model (ΛCDM), in which the universe is expanding, had an early hot dense phase (the Big Bang), and is currently undergoing accelerated expansion attributed to a cosmological constant (interpreted by many as dark energy). The value and physical interpretation of Λ remain active areas of research and debate. The Hubble tension - a statistically significant discrepancy between measurements of the universe's expansion rate obtained by different methods - is an unresolved empirical problem within the standard model. See Hubble Tension - Debate.

There is broad consensus in the physics community that general relativity is the best-confirmed classical description of gravitation across tested scales and regimes. See General Relativity - Physics Consensus. Debate continues at boundaries: the interpretation of singularities, the nature of dark energy, the correct theory of quantum gravity, and the resolution of the black hole information paradox remain open. See Black Hole Information Paradox - Debate.

• Standard Interpretation - GR as a complete and accurate classical theory of gravitation, with incompleteness arising only at quantum scales.
• Modified Gravity - Proposals such as MOND (Modified Newtonian Dynamics), scalar-tensor theories (Brans-Dicke), and f(R) gravity that extend or modify the Einstein field equations to account for anomalies without invoking dark matter or dark energy.
• Emergent Gravity - The view, associated with work by Erik Verlinde and others, that gravity is not a fundamental interaction but an emergent thermodynamic or entropic phenomenon.

• General Relativity - History
• General Relativity - Physics Consensus
• Quantum Gravity - Debate
• Black Hole Information Paradox - Debate
• Hubble Tension - Debate
• Special Relativity
• Quantum Gravity
• Quantum Mechanics
• Cosmology
• Dark Energy
• Dark Matter
• Black Holes
• Gravitational Waves

^{2) 3) 4) 5) 6) 7) 8)}