发表机构
Taras Shevchenko National University of Kyiv; Igor Sikorsky Kyiv Polytechnic Institute; Pidstryhach Institute for Applied Problems of Mechanics and Mathematics（基辅塔拉斯舍甫琴科国立大学; 伊戈尔西科尔斯基基辅理工学院; 皮德斯特里亚赫应用力学与数学问题研究所）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文研究广义相对论中带最小耦合标量场的球对称静态构型的线性稳定性，采用新打靶法提取指数增长模式特征值，证实小标量电荷下存在不稳定模式。
AI 中文摘要
在广义相对论中，静态球对称渐近平坦且带有最小耦合标量场的构型通常具有裸奇点。我们研究了在幂律标量场势情形下，这些构型对径向（单极）扰动的线性稳定性。我们采用了一种新的打靶方法，该方法提取对应于扰动指数增长模式的特征值。问题被简化为一个具有正则化有效势的发散形式的二阶“主”方程。我们证实了之前的结果，表明对于初始静态构型足够小的标量电荷，不稳定性模式是存在的。
英文摘要
Static spherically symmetric asymptotically flat configurations in General Relativity with a minimally coupled scalar field typically possess naked singularities. We study a linear stability of these configurations against radial (monopole) perturbations in case of power-law scalar field potentials. We employ a new shooting method that extracts the eigenvalues corresponding to the exponentially growing modes of the perturbation. The problem is reduced to one second order ``master'' equation in a divergent form with a regularized effective potential. We confirm our previous results showing that instability modes exist for sufficiently small scalar charges of the initial static configurations.
Comments4 pages, 5 figures, XXVI Gamow International Astronomical Conference, 17-26 August 2026, Odesa, Ukraine
