= 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 are
$$
\boxed{M\quad\text{and}\quad J,\qquad a=J/M.}
$$
The <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.
Back to article page
