How Do Spherical Black Holes Grow Monopole Hair?
Abhishek Hegade K. R., Elias R. Most, Jorge Noronha, Helvi Witek and, Nicolas Yunes
TL;DR
This paper investigates how scalar hair develops during black hole formation in modified gravity theories, demonstrating that scalar radiation emission is essential for the growth of monopole hair as the horizon forms.
Contribution
It provides a rigorous proof linking scalar hair growth to horizon formation and offers analytical and numerical solutions in specific collapse scenarios within scalar Gauss-Bonnet gravity.
Findings
Scalar hair growth is tied to event horizon formation.
Scalar radiation emission is necessary for monopole hair development.
Analytical solution for scalar field in Oppenheimer-Snyder collapse.
Abstract
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 paper, we study 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. We prove this result rigorously in general first for a large class of modified theories, and then we exemplify the results by studying the temporal evolution of the scalar field in scalar Gauss-Bonnet gravity in two backgrounds: (i) a collapsing…
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