Density of hyperbolicity for rational maps

Let $f:\hat{\mathbb{C}}\rightarrow \hat{\mathbb{C}}$ be a rational map of degree $d\geqslant 2$, and let $\mathrm{Rat}_{d}$ denote the space of Möbius equivalence classes of rational maps of degree $d$. A rational map is hyperbolic if it has a smooth conformal metric on a neighborhood of its Julia set $J(f)$ that is uniformly expanded by its derivative on $J(f)$. Density of hyperbolicity. The set of hyperbolic rational maps is open and dense in the space $\mathrm{Rat}_{d}$. Openness is known, but density is known only in several special families, including real polynomials.