| General relativity | |
|---|---|
| Name | General relativity |
| Caption | Albert Einstein, author of the field equations |
| Author | Albert Einstein |
| Introduced | 1915 |
| Institutions | Prussian Academy of Sciences, Institute for Advanced Study |
| Related | Special relativity, Quantum field theory, Cosmology |
General relativity
General relativity is the geometric theory of gravitation published by Albert Einstein in 1915 that describes gravity as the curvature of spacetime caused by energy and momentum. It replaced Isaac Newton's Newtonian conception of a force acting at a distance and provides the modern framework for cosmology, astrophysics, and precision tests that intersect with Quantum mechanics and ongoing efforts in quantum gravity. Its reconciliation with quantum theory remains one of the central problems in theoretical physics.
General relativity originated from attempts by Albert Einstein to extend Special relativity to include gravity and acceleration. Early conceptual precursors include the equivalence principle, articulated by Einstein, and mathematical tools developed by Bernhard Riemann and Gregorio Ricci-Curbastro (the Ricci calculus). The 1915 publication of the Einstein field equations followed earlier work on the perihelion advance of Mercury and exchanges with contemporaries such as David Hilbert, Marcel Grossmann, and Hermann Weyl. The theory gained empirical credibility after the 1919 Eddington expedition measurements of light deflection during a solar eclipse and subsequently through observations by institutions like Royal Observatory, Greenwich and modern facilities such as the Hubble Space Telescope and the Event Horizon Telescope.
The mathematical basis of general relativity is differential geometry, using a semi-Riemannian metric tensor g_{μν} on a four-dimensional manifold to represent spacetime. Central objects include the Riemann curvature tensor, Ricci tensor R_{μν}, and the Einstein tensor G_{μν}. The Einstein field equations, G_{μν} + Λg_{μν} = (8πG/c^4) T_{μν}, relate geometry to matter through the stress–energy tensor T_{μν} and the cosmological constant Λ. Solutions to these nonlinear partial differential equations include the Schwarzschild metric, Kerr metric, FLRW metric, and the Reissner–Nordström metric, which model isolated masses, rotating black holes, homogeneous cosmologies, and charged bodies respectively. Techniques from tensor calculus, variational principles (the Einstein–Hilbert action), and numerical relativity carried out with supercomputers are essential for deriving and simulating solutions.
General relativity predicts phenomena absent in Newtonian gravity, including gravitational time dilation, gravitational redshift, light deflection, and frame-dragging (the Lense–Thirring effect). Precision tests include the Pound–Rebka experiment on gravitational redshift, the perihelion precession of Mercury, the Shapiro time delay measured via Voyager and radio links to spacecraft, and gyroscope measurements by the Gravity Probe B mission. The detection of gravitational waves by the LIGO and VIRGO collaborations provided direct confirmation of dynamical spacetime and validated predictions for inspiraling binary systems made by post-Newtonian approximations and numerical relativity. Strong-field tests around supermassive compact objects have been informed by observations of the Galactic Center and the imaging of M87* by the Event Horizon Telescope.
Exact solutions such as the Schwarzschild solution and Kerr solution predict horizons and causal structure that permit black holes. Theoretical work by Roger Penrose and Stephen Hawking produced the Penrose–Hawking singularity theorems, showing conditions under which singularities arise. Concepts of event horizons, trapped surfaces, and the laws of black hole mechanics link thermodynamic ideas to geometry; Hawking radiation—a semiclassical prediction combining quantum field theory in curved spacetime by Stephen Hawking—implies black holes have temperature and entropy proportional to area (Bekenstein–Hawking entropy). The study of singularities and horizon microphysics motivates quantum gravity approaches.
Applied to a homogeneous and isotropic universe via the FLRW metric, general relativity yields the Friedmann equations, governing cosmic expansion. Early solutions by Alexander Friedmann and Georges Lemaître anticipated an expanding universe confirmed by Edwin Hubble's redshift–distance relation. Incorporating Λ leads to models with accelerated expansion consistent with observations of Type Ia supernovae and cosmic microwave background anisotropies measured by missions such as COBE, WMAP, and Planck. Problems like the horizon problem and flatness problem motivated cosmic inflation by Alan Guth and others, which interfaces with quantum field processes in the early universe.
General relativity's classical continuum description conflicts with quantum principles, prompting programs for quantum gravity such as canonical quantum gravity, loop quantum gravity, and string theory. Semiclassical methods—quantum field theory in curved spacetime—predict effects like Hawking radiation and vacuum polarization in strong gravity, studied using methods from renormalization and effective field theory by researchers at institutions like CERN and Perimeter Institute for Theoretical Physics. The AdS/CFT correspondence from string theory offers a holographic perspective relating a gravitational theory in anti-de Sitter space to a conformal field theory, impacting black hole thermodynamics and quantum information considerations (e.g., the AMPS firewall paradox). Experimental tests of quantum gravity remain challenging; proposals include tabletop tests of quantum superpositions of mass distributions and observations of Planck-scale modifications in high-energy astrophysical data.
Although fundamentally a theory of gravitation, general relativity has practical consequences: precise timing corrections from gravitational time dilation are critical for the Global Positioning System operated by United States Department of Defense and commercial systems. Relativistic models underpin spacecraft navigation for missions by NASA and ESA, and gravitational lensing is used as a tool in observational cosmology and in searches for dark matter via projects like the Sloan Digital Sky Survey. Advances in numerical relativity have enabled waveform templates used by LIGO Scientific Collaboration for gravitational-wave astronomy, inaugurating multimessenger astrophysics in conjunction with observatories such as Fermi Gamma-ray Space Telescope and IceCube Neutrino Observatory.
Category:Theory of relativity Category:Gravitation