发表机构
Kavli Institute for Astronomy and Astrophysics, Peking University; School of Science, Jiangsu University of Science and Technology; Center for Quantum Spacetime, Sogang University（北京大学天体物理与天文研究所; 江苏科技大学理学院; 西江大学量子时空中心）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文研究极端EEH标量理论中标量化黑洞，通过存在曲线和熵函数方法揭示标量毛在极端极限下的次级性质及标量化区域边界。
AI 中文摘要
我们研究了在具有两个与麦克斯韦项耦合的标量耦合的通用爱因斯坦-欧拉-海森堡（EEH）-标量理论中的带标量毛的极端黑洞。其中一个是指数耦合，耦合常数为$\alpha$，另一个是其多项式耦合。我们首先在EEH黑洞的冷（C）视界上构建标量化黑洞，该黑洞由质量$M$和磁荷$P$描述，在线性层面通过存在曲线$\alpha_n(q)$（其中$q=P/M$）以及作为完全反作用解来构建。当趋近极端性（$q=q_e$）时，所有存在曲线累积，遵循$\alpha_n-\alpha_c\sim 1/\ln^2(q_e-q)$，趋向于由近视界（AdS$_2\times S^2$）喉部的Breitenlohner-Freedman界限确定的临界分支$\alpha_c$。我们获得了具有恒定次级毛的标量化极端黑洞（SEBH），并且它可以从作用于近视界喉部的熵函数方法中精确恢复。其熵是一个吸引子不变量，与渐近模量无关，因此标量毛保持次级性。利用这个恒定标量，我们进一步寻找在零渐近标量（$\phi_\infty=0$）下保持其电荷$Q_s$的带标量毛的SEBH。在$(q,\alpha)$平面中，我们观察到这些极端解占据$q\ge q_e$。因此，存在于$q\le q_e$的存在曲线$\alpha_n(q)$和极端分支从相反两侧界定了标量化区域，并且它们仅在$q=q_e$处相遇。
英文摘要
We investigate extremal black holes with scalar hair in the generic Einstein-Euler-Heisenberg (EEH)-scalar theory with two scalar couplings to the Maxwell term. One is an exponential coupling with coupling constant $α$ and the other is its polynomial coupling. We first construct scalarized black holes on the cold (C)-horizon of EEH black holes described by mass $M$ and magnetic charge $P$ both at the linear level, through the existence curves $α_n(q)$ with $q=P/M$, and as fully backreaction solutions. As extremality ($q=q_e$) is approached, all existence curves accumulate, following $α_n-α_c\sim 1/\ln^2(q_e-q)$, at the critical branch $α_c$ fixed by the Breitenlohner-Freedman bound for the near-horizon (AdS$_2\times S^2$) throat. We obtain scalarized extremal black hole (SEBH) with constant secondary hair and it is recovered exactly from the entropy function approach working on the near-horizon throat. Its entropy is an attractor invariant, being independent of the asymptotic modulus, so the scalar hair remains secondary. Exploiting this constant scalar, we seek further SEBHs with scalar hair keeping its charge $Q_s$ for the zero asymptotic scalar ($ϕ_\infty=0$). In the $(q,α)$ plane, we observe that these extremal solutions occupy $q\ge q_e$. Hence, the existence curves $α_n(q)$ existing for $q\le q_e$ and the extremal branches bound the scalarized domain from opposite sides and they meet only at $q=q_e$.
Comments31 pages, 9 figures
