Which equation in general relativity predicted the existence of black-holes ?

In the context of general relativity, the existence of black holes is predicted by the Einstein field equations (EFE). These equations, formulated by Albert Einstein in 1915, relate the geometry of spacetime to the distribution of mass and energy within it.

Specifically, the solution to the Einstein field equations known as the Schwarzschild metric, discovered by Karl Schwarzschild in 1916, describes the gravitational field outside a spherical mass and predicts the existence of black holes. This solution is a vacuum solution to the Einstein field equations, meaning it applies in regions where the stress-energy tensor (T_{\mu \nu}) is zero123.