How do spherical black holes grow monopole hair?

Black holes in certain modified gravity theories that contain a scalar field coupled to curvature invariants are known possess (monopole) hair while non-black-hole spacetimes (like neutron stars) do not. Therefore, as star collapses black hole, must grow until it settles the stationary hole solution with hair. In this paper, we study process detail and show growth of is tied appearance event horizon (before an apparent forms), which forces modes would otherwise (in future) become divergent be radiated away. We prove result rigorously general first for large class theories, then exemplify results by studying temporal evolution Gauss-Bonnet two backgrounds: (i) collapsing Oppenheimer-Snyder background, (ii) background. case (i), find exact analytically, solve numerically, both cases supporting conclusion presented above. Our suggest emission burst radiation necessary condition formation gravity.