CSC Bergman metrics are Einstein on pseudoconvex domains

Let $\mathrm{\Omega }\subset {\mathbb{C}}^n$($n\ge 3$) be a pseudoconvex domain with a smooth strongly pseudoconvex boundary point. We prove that if the Bergman metric of $\mathrm{\Omega }$ has constant scalar curvature, then it is necessarily Kähler–Einstein.