Which theory of gravity first predicted black holes as solutions to its field equations?

Which theory of gravity first predicted black holes as solutions to its field equations? General relativity did.

Albert Einstein’s general theory of relativity, published in its final form in 1915, describes gravity as the curvature of spacetime produced by mass and energy. Its field equations admit solutions in which matter can collapse so intensely that an event horizon forms, creating what we now call a black hole.

Karl Schwarzschild found the first exact black-hole solution in 1916, only months after Einstein presented the theory. The Schwarzschild solution describes the spacetime outside a spherical, nonrotating, uncharged mass and includes a characteristic radius now called the Schwarzschild radius. Later work showed that rotating and charged black holes also arise from general relativity’s equations.

Newtonian gravity can describe an object whose escape speed exceeds the speed of light, and John Michell and Pierre-Simon Laplace discussed such dark stars centuries ago. However, Newtonian theory has no spacetime, event horizons, or relativistic treatment of light, so those objects were not black holes in the modern sense. String theory and quantum mechanics may help explain deeper physics, but neither first predicted the classical black-hole solutions.