How Do Black Holes Grow Hair?

Black holes in certain modified gravity theories that contain a scalar field coupled to curvature invariants are known to possess (monopole) scalar hair while non-black-hole spacetimes (like neutron stars) do not. Therefore, as a neutron star collapses to a black hole, scalar hair must grow until it settles to the stationary black hole solution with (monopole) hair. In this talk, I will describe this process in detail and show that the growth of scalar hair is tied to the appearance and growth of the event horizon (before an apparent horizon forms), which forces scalar modes that would otherwise (in the future) become divergent to be radiated away. I will then outline a proof of this result for a large class of modified theories. I will also present the results for the temporal evolution of the scalar field numerically in scalar Gauss-Bonnet gravity in a collapsing neutron star background as an example to explain the physical process by which the scalar hair grows.These results suggest that the emission of a burst of scalar field radiation is a necessary condition for black hole formation in a large class of modified theories of gravity.