带有两个薄壳的黑洞周围物质诱导标量化的集体 onset
Collective Onset of Matter-Induced Scalarization around a Black Hole with Two Thin Shells
- Tohoku Gakuin University（东北学院大学）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
该研究探讨被两个薄壳包围的静态黑洞的物质诱导标量化线性 onset，推导了集体失稳的有限秩条件及临界标量云，数值验证了超阈值的增长模式，还分析了精确无标量背景下的符号转变。
AI中文摘要：
我们研究被两个空间分离的薄物质壳包围的静态黑洞的物质诱导标量化的线性 onset。我们假设在无标量背景上共形物质耦合为1，且其对数导数在该处消失。此时标量扰动在一阶近似下与度规和物质扰动解耦，而壳的不变表面迹在标量方程中产生奇异项。对于壳之间不存在体标量有效质量项的静态球对称黑洞外部，onset 简化为有限秩条件：$$1-a_1-a_2+(1-\boldsymbol{\times})a_1a_2=0, \boldsymbol{\times}=\frac{{\boldsymbol{\times}}(R_2)}{{\boldsymbol{\times}}(R_1)}$$，其中 $a_j$ 是第 $j$ 个壳在相同背景下以单壳阈值归一化的吸引强度，${\boldsymbol{\times}}$ 为静态径向阻力。该关系表明，两个单独处于亚临界状态的壳可集体使无标量黑洞失稳。我们推导了临界标量云的闭合形式，并在施瓦西探针问题中数值验证：超过阈值后会出现具有有限增长率的增长模式。对于由两个以色列壳连接的三个施瓦西区域组成的精确无标量背景，我们分别推导了静态 onset 条件和对应的临界云，精确的以色列迹还表现出符号转变，其轻壳极限出现在施瓦西光子球处。
英文摘要：
We study the linear onset of matter-induced scalarization for a static black hole surrounded by two spatially separated thin matter shells. We assume that the conformal matter coupling is unity on the scalar-free background and that its logarithmic derivative vanishes there. The scalar perturbation then decouples from the metric and matter perturbations at first order, while the invariant surface traces of the shells give singular terms in the scalar equation. For a static spherical black-hole exterior with no bulk scalar effective-mass term between the shells, the onset reduces to the finite-rank condition $$ 1-a_1-a_2+(1-χ)a_1a_2=0, \qquad χ=\frac{{\cal S}(R_2)}{{\cal S}(R_1)}, $$ where $a_j$ is the attractive strength of shell $j$ normalized by its one--shell threshold on the same background and ${\cal S}$ is the static radial resistance. This relation shows that two individually subcritical shells can collectively destabilize the scalar-free black hole. We derive the critical scalar cloud in closed form and verify numerically, in the Schwarzschild probe problem, that a growing mode with a finite growth rate appears beyond the threshold. For an exact scalar-free background consisting of three Schwarzschild regions joined by two Israel shells, we separately derive the static onset condition and the corresponding critical cloud. The exact Israel trace also exhibits a sign transition whose light-shell limit occurs at the Schwarzschild photon sphere.
