General Theory of Relativity

General Theory of Relativity
Simulating eXtreme Spacetimes Lensing (SXS) · CC BY-SA 4.0 · source
Name	General Theory of Relativity
Caption	Albert Einstein, 1921
Field	Albert Einstein; Isaac Newton; Karl Schwarzschild
Introduced	1915
Notable works	Annalen der Physik; The Meaning of Relativity

Contents

General Theory of Relativity The General Theory of Relativity is a theory of gravitation published in 1915 that extended Special relativity and modified Isaac Newton's law of universal gravitation, providing a new description of spacetime, gravitation, and inertia. Developed principally by Albert Einstein with mathematical contributions from Marcel Grossmann and responses from contemporaries such as David Hilbert and Hermann Minkowski, it revolutionized understanding across physics and astronomy, influencing research at institutions like Princeton University, University of Göttingen, and Kavli Institute for Theoretical Physics.

History and development

Einstein announced the theory in a series of papers culminating in 1915 in Annalen der Physik, following earlier work on Special relativity (1905) and correspondence with mathematicians including Marcel Grossmann and Felix Klein, and feedback from physicists such as Max Planck, Hendrik Lorentz, and Wilhelm Wien. The 1916 review by Einstein and subsequent solutions by Karl Schwarzschild (1916) and analyses by Arthur Eddington and Subrahmanyan Chandrasekhar helped propagate the theory through communities at Royal Observatory, Greenwich, Cambridge University, and Yale University. Key developments intersected with events like World War I and institutions such as Kaiser Wilhelm Society and Royal Society, while later refinements involved researchers at California Institute of Technology, Harvard University, and Max Planck Institute for Gravitational Physics.

The theory is formulated using the mathematics of Riemannian geometry, tensor calculus developed by Gregorio Ricci-Curbastro and Tullio Levi-Civita, and differential geometry popularized in physics by Hermann Minkowski and Élie Cartan. Central equations are the Einstein field equations, relating the stress–energy tensor (as used in works by J. Robert Oppenheimer and Lev Landau) to the spacetime curvature described by the Ricci curvature tensor and Einstein tensor, employing tools from Lorentz group representation theory and variational principles akin to the Euler–Lagrange equation used in mechanics by Joseph-Louis Lagrange. Calculations often use coordinate systems introduced by Karl Schwarzschild, Roy Kerr, and Friedrich Wilhelm Bessel-influenced astrometry; exact solutions draw on methods applied by Georges Lemaître and Alexander Friedmann.

General relativity posits that matter and energy determine spacetime curvature, with free-falling bodies following geodesics as in analyses by Arthur Eddington and Bernard Schutz, predicting phenomena including gravitational time dilation observed in contexts studied by J. C. Maxwell-inspired electromagnetism and by experiments at National Institute of Standards and Technology. It predicts gravitational lensing verified in observations linked to Edwin Hubble and interpreted using techniques developed by Subrahmanyan Chandrasekhar, frame-dragging later modeled by Josef Lense and Hans Thirring, and black hole properties formalized through work by Roger Penrose, Stephen Hawking, and Roy Kerr. Cosmological implications connect to the Friedmann equations of Alexander Friedmann and the expanding universe concept promoted by Georges Lemaître and Edwin Hubble.

Early tests included the 1919 solar eclipse expedition led by Arthur Eddington and Frank Dyson confirming light deflection, and perihelion precession of Mercury reconciled with calculations by Urbain Le Verrier and subsequent astrophysical analyses at Observatoire de Paris. Precision tests involve timing experiments with Pound–Rebka experiment-related techniques developed at Harvard University and global positioning refinements implemented by United States Department of Defense systems influenced by Navstar GPS research. Gravitational redshift, time dilation, and frame-dragging have been measured in missions by Gravity Probe B and radio timing of pulsars including discoveries by Russell Hulse and Joseph Taylor, while gravitational waves predicted by the theory were detected by LIGO and Virgo Collaboration, with multimessenger observations coordinated with European Southern Observatory and Fermi Gamma-ray Space Telescope.

Exact and approximate solutions include the Schwarzschild solution (black holes, stellar collapse studies by J. Robert Oppenheimer), the Kerr metric for rotating bodies (expanded by Roy Kerr and analyzed by Brandon Carter), the Friedmann–Lemaître–Robertson–Walker metric for homogeneous cosmologies (used by Alexander Friedmann and Georges Lemaître), and perturbative approaches applied in cosmological structure formation modeled by Jerry Ostriker and James Peebles. The theory underlies models of Big Bang cosmology tied to observations by George Gamow and interpretation of the Cosmic Microwave Background measured by COBE, WMAP, and Planck (spacecraft), and informs singularity theorems developed by Roger Penrose and Stephen Hawking that intersect with proposals from Edward Witten and Juan Maldacena in quantum gravity research.

Applications include precise orbit prediction for spacecraft by teams at NASA and European Space Agency, timekeeping and navigation reliant on relativistic corrections applied in Navstar GPS operations and satellite systems designed at Jet Propulsion Laboratory, and relativistic modeling used in high-energy astrophysics at CERN and Fermi National Accelerator Laboratory. The theory has inspired technologies emerging from institutions such as MIT and Stanford University in fields overlapping with gravitational-wave detectors by LIGO Laboratory and sensor development at Max Planck Institute for Gravitational Physics, while driving fundamental research programs at Perimeter Institute and Kavli Institute for Cosmological Physics that feed into applied advances in geodesy and observational astronomy at National Radio Astronomy Observatory.