标题： 带电高斯-博内黑洞支持非最小耦合标量云：近临界 regime 的解析处理 显示英文标题

标题： Charged Gauss-Bonnet black holes supporting non-minimally coupled scalar clouds: Analytic treatment in the near-critical regime

摘要： 最近的数值研究揭示了一个物理上引人注目的事实，即电荷与质量比大于临界值$(Q/M)_{\text{crit}}=\sqrt{2(9+\sqrt{6})}/5$的带电黑洞可以支持由与弯曲时空的高斯-博内不变量非最小负耦合的标量场组成的毛发物质配置。 使用{\it 分析的}技术，我们探讨了近临界$Q/M\gtrsim (Q/M)_{\text{crit}}$范围内组合带电黑洞-非最小耦合线性化无质量标量场配置的物理和数学性质。 特别是，我们推导出一个解析共振公式，该公式描述了组合爱因斯坦-麦克斯韦-非最小耦合标量场系统沿理论的{\it 存在线}的电荷依赖性无量纲耦合参数$\bar\eta_{\text{crit}}=\bar\eta_{\text{crit}}(Q/M)$，这是一个将无毛的雷西纳-诺德斯特伦黑洞与带毛的带电黑洞-标量场配置分隔开的关键边界。 此外，明确展示了本文针对组合爱因斯坦-麦克斯韦标量理论得到的大耦合$-\bar\eta_{\text{crit}}(Q/M)\gg1$解析结果与相应黑洞-场共振谱的直接数值计算结果非常吻合。 显示英文摘要

摘要： Recent numerical studies have revealed the physically intriguing fact that charged black holes whose charge-to-mass ratios are larger than the critical value $(Q/M)_{\text{crit}}=\sqrt{2(9+\sqrt{6})}/5$ can support hairy matter configurations which are made of scalar fields with a non-minimal negative coupling to the Gauss-Bonnet invariant of the curved spacetime. Using {\it analytical} techniques, we explore the physical and mathematical properties of the composed charged-black-hole-nonminimally-coupled-linearized-massless-scalar-field configurations in the near-critical $Q/M\gtrsim (Q/M)_{\text{crit}}$ regime. In particular, we derive an analytical resonance formula that describes the charge-dependence of the dimensionless coupling parameter $\bar\eta_{\text{crit}}=\bar\eta_{\text{crit}}(Q/M)$ of the composed Einstein-Maxwell-nonminimally-coupled-scalar-field system along the {\it existence-line} of the theory, a critical border that separates bald Reissner-Nordstr\"om black holes from hairy charged-black-hole-scalar-field configurations. In addition, it is explicitly shown that the large-coupling $-\bar\eta_{\text{crit}}(Q/M)\gg1$ analytical results derived in the present paper for the composed Einstein-Maxwell-scalar theory agree remarkably well with direct numerical computations of the corresponding black-hole-field resonance spectrum.