"Black Holes as Probes for Ultralight Dark Matter"
In a scenario where non-gravitational dark matter interactions are negligible, it is natural to think of black holes as probes because of their very strong gravitational fields. We choose to focus on wave dark matter because an oscillating massive scalar endows a black hole with hair. I will identify the relevant length scales of the problem and study the scalar field profile analytically rather than numerically, to better capture the different behaviors at different scales. I will emphasize near-horizon physics, where imposing causal boundary conditions can affect the solution at much larger scales. Accounting for the self-gravity of the scalar cloud, I will study the possibility of dark matter forming a soliton around the black hole. In this case, requiring stability of the system forces a hierarchy of length scales, which I will discuss.