发表机构
Institute for Basic Science (IBS); Université Paris-Saclay, CNRS/IN2P3, IJCLab（基础科学研究院; 巴黎萨克雷大学，法国国家科学研究中心/法国国家粒子物理研究所，IJCLab）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文在Horndeski引力扩展理论中开发新方法，构建带原生毛发的非互易黑洞精确解，研究其稳定性，发现代表性标量毛发解在考虑的扰动模式下线性稳定。
AI 中文摘要
我们开发了一种新颖的系统方法，用于在具有平移对称性和Z2对称性的Horndeski引力扩展理论中构建精确、静态且渐近平坦的黑洞解。与以往研究不同，我们的方法不依赖于限制性的互易条件g_tt g_rr = -1，允许以两个独立度规函数为特征的更一般几何结构。所得解空间包含两种性质截然不同的毛发，源自该理论的不同分支：一个分支以计时毛发（khronometric hair）为特征，另一个以真正的标量毛发为特征。在两种分支中，标量剖面均定义了非平凡的优先叶状结构，但平移对称性的诺特定理流及相关传播自由度，对于前者是平凡的，对于后者则非零。我们主要聚焦于第二个分支，推导了若干不同族的精确黑洞解。总体而言，这些解是奇异的，且与独立标量荷相关的原生标量毛发共存。不过，我们证明它们可被正则化以产生正则黑洞或孤子构型，此时标量毛发变为次生的。我们进一步通过分析轴向扇区和偶宇称扇区的单极（ℓ=0）模式，研究这些解在线性扰动下的稳定性性质。对于具有标量毛发的代表性解，扰动分析提供了所考虑模式下线性稳定的证据。
英文摘要
We develop a novel systematic method for constructing exact, static, and asymptotically flat black-hole solutions in shift-symmetric and $Z_2$-symmetric beyond Horndeski theories. In contrast to previous studies, our approach does not rely on the restrictive reciprocal condition $g_{tt}g_{rr}=-1$, allowing for more general geometries characterized by two independent metric functions. The resulting solution space contains two qualitatively distinct types of hair originating from different branches of the theory. One branch is characterized by khronometric hair, while the other by genuine scalar hair. In both, the scalar profile defines a nontrivial preferred foliation, but the shift-symmetry Noether current and the associated propagating degree of freedom are trivial for the former and nonvanishing for the latter. Focusing mainly on the second branch, we derive several distinct families of exact black-hole solutions. In general, these solutions are singular and exhibit primary scalar hair associated with an independent scalar charge. Nevertheless, we demonstrate that they can be regularized to yield regular black-hole or solitonic configurations, for which the scalar hair becomes secondary. We further investigate the stability properties of these solutions under linear perturbations by analyzing the axial sector and the monopole $(\ell=0)$ mode of the even-parity sector. For representative solutions with scalar hair, the perturbative analysis provides evidence for linear stability under the modes considered.
Comments54 pages, 5 figures
