 Solution

An isolated uncharged collapsing star initially has higher multipole moments and possibly time-dependent motion. The changing exterior emits gravitational waves, carrying away energy and nonspherical structure. Perturbations of the final black hole decay, so the late exterior is expected to approach a stationary spacetime.

Under the regularity, asymptotic flatness, and connected-horizon hypotheses of the black-hole uniqueness theorem, a stationary four-dimensional vacuum black hole is a Kerr black hole. Since the electric charge is zero, its intrinsic parameters areThe black-hole no-hair theorem expresses the loss of independently specifiable higher multipoles: those of the final Kerr black hole are determined by $M,J$. The direction of the rotation axis can be chosen by orienting the coordinates and is not an additional intrinsic parameter of the geometry.

This is a statement about the settled, isolated exterior in classical general relativity, conditional on settling and the hypotheses of the black-hole uniqueness theorem. It does not describe the entire radiating collapse spacetime with only two numbers, nor does it extend unchanged to additional long-range matter fields.