Is it possible the no-hair paradigm is violated when a black hole undergoes an instability? Employing massless charged scalar perturbations, we address this question within the context of conformally invariant Einstein-Maxwell theory for some allowed d-dimensional ($d=4n+4$ with conformal parameter $n=0,1,2,...$) topological small AdS black-holes. We provide numerical analyses that show the non trivial scalar hairy black hole solutions to include planar and spherical horizon topologies in higher dimensions with an even conformal parameter n. It is also shown that the solutions presented here cannot be considered as scalar hairs for a Reissner-Nordstrom background. As a result, for d-dimensional small AdS black holes in the presence of a conformally invariant Maxwell source, the no-scalar hair paradigm seems to be supported.

当黑洞不稳定时，有可能违反无毛范例吗？利用无质量的带电标量摄动，我们针对某些允许的d维（共形不变的Einstein-Maxwell理论）解决了这个问题$d=4ñ+4$ 保形参数 $ñ=0，\mathrm{1个}，2，。。。$）拓扑小AdS黑洞。我们提供的数值分析显示了非平凡的标量毛状黑洞解决方案，其中包括具有偶数保形参数n的更高维度的平面和球形层状拓扑。还表明，对于Reissner-Nordstrom背景，此处介绍的解决方案不能视为标量头发。结果，对于存在共形不变的麦克斯韦源的d维小AdS黑洞，似乎支持无标量头发范例。