Schwarzschild's Solution (1916)
Shortly after Einstein published General Relativity, Karl Schwarzschild found the first exact solution to the field equations. This solution describes the spacetime geometry outside a spherical, non-rotating mass. It confirms the existence of a horizon at $r_s$, but unlike Newtonian physics, it arises from spacetime curvature, not just kinetic energy limits.
Limitations of Newtonian Physics
While Newtonian physics predicts a 'dark star,' it fails to capture the full nature of a black hole. It does not account for time dilation, the bending of light paths in curved space, or the singularity at the center. General Relativity is required for a complete description.