Which 1916 solution describes spacetime outside a spherical non-rotating mass?

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The 1916 solution describing spacetime outside a spherical, non-rotating mass is the Schwarzschild metric.

Karl Schwarzschild found the solution in 1915 and published it in January 1916, shortly after Einstein’s field equations appeared. It is an exact vacuum solution of general relativity under assumptions of spherical symmetry, zero charge, zero angular momentum, and no cosmological constant. Johannes Droste independently obtained the same solution in 1916.

The metric describes the exterior gravitational field of objects ranging from planets and stars to idealized black holes. Its characteristic length is the Schwarzschild radius, 2GM/c². If a non-rotating, uncharged object is compressed inside that radius, the solution describes a black hole with an event horizon.

The Kerr metric is the neighboring case for rotating masses, while the Reissner–Nordström metric includes electric charge. The Schwarzschild metric is also the basis for classic predictions such as gravitational time dilation, light bending, and the unstable photon sphere.

Source: Wikipedia · fact-checked Sept. 2026

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