General Theory of Relativity

The General Theory of Relativity, completed in 1915 after nearly a decade of arduous mathematical development, extends the principle of relativity to non-inertial (accelerating) reference frames. Its central insight is the equivalence principle: locally, the effects of a gravitational field are indistinguishable from those of acceleration. This observation, combined with the geometry of Riemannian manifolds, led to the Einstein field equations — ten coupled, nonlinear partial differential equations relating the curvature of spacetime (encoded in the Einstein tensor) to the distribution of matter and energy (encoded in the stress–energy tensor).

The theory makes a number of predictions that depart from Newtonian gravity. The precession of Mercury’s perihelion, an anomaly of 43 arcseconds per century that Newtonian mechanics could not fully explain, emerged naturally from the field equations without any additional assumptions. The deflection of starlight by the Sun’s gravitational field — measured during the solar eclipse of 1919 by Arthur Eddington — provided the first dramatic experimental confirmation and brought Einstein international renown. Subsequently, the theory has been confirmed by gravitational redshift measurements, frame-dragging effects observed by Gravity Probe B, and, most recently, the direct detection of gravitational waves by the LIGO–Virgo collaboration.

Beyond observational tests, general relativity underpins our understanding of black holes, neutron stars, gravitational lensing, and the large-scale structure and dynamics of the universe. The Friedmann–Lemaître–Robertson–Walker solutions to the field equations provide the mathematical backbone of modern cosmology, including the Big Bang model. This project collects the foundational papers, the derivation of key solutions (Schwarzschild, Kerr), and ongoing investigations into the quantum regime where general relativity is expected to break down.