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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.

An isolated collapse emits transient matter and gravitational waves. The exterior is expected to settle to an asymptotically flat stationary spacetime. Because the star is uncharged, the black-hole uniqueness theorem identifies the regular final state with a Kerr black hole. Its higher multipole moments are fixed by its conserved charges: the black-hole no-hair theorem leaves only the total mass $M$ and angular momentum $J$. Thus the late-time spacetime is characterized by $M$ and $J$.