Schwarzschild solution

The Schwarzschild solution is the first exact solution of Einstein's field equations, found by Karl Schwarzschild in 1916 within months of the theory's publication, while he was serving on the Russian front. It describes the spacetime outside a non-rotating, perfectly spherical mass, such as an idealized star, planet, or black hole. It is the simplest realistic gravity field in general relativity and the workhorse for testing the theory.

From this single solution flow many of the famous predictions. It explains the small extra twist in Mercury's orbit that Newton's gravity could not, predicts how clocks slow and light reddens as they climb out of a gravity well, and describes how a light ray bends as it skims past the Sun. For weak gravity it reproduces Newton's familiar inverse-square law, but it adds tiny corrections that have all been confirmed.

The solution also revealed something startling. If a mass is squeezed within a certain critical radius, the geometry becomes so extreme that even light cannot escape, producing a black hole. The boundary of no return sits at the Schwarzschild radius, proportional to the mass. For decades black holes were dismissed as a mathematical curiosity, but we now observe them directly, including the imaged shadow of the black hole at the center of galaxy M87.