发表机构
Scuola Superiore Meridionale; INFN sezione di Napoli; Southern Denmark University; Universidade de Aveiro; Universidade Federal do Pará（南方高等学院; 意大利国家核物理研究所那不勒斯分部; 南丹麦大学; 阿威罗大学; 帕拉联邦大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
研究标量波动对史瓦西黑洞的反作用，在小耦合 regime 下通过评估应力 - 能量张量求解爱因斯坦方程，解析确定准共振频率，获得度规微扰等表达式，推导视界演化，明确相关近似和展开同时有效的区域。
AI 中文摘要
我们通过解析确定了具有质量$\mu$的球对称大质量复标量准束缚态对初始引力半径为$r_0$的史瓦西黑洞的主导反作用。在小耦合 regime，$r_0\mu\ll1$下，我们评估了基本标量$s$波的应力 - 能量张量，并在ingoing Eddington - Finkelstein坐标中通过其振幅的二次项求解爱因斯坦方程。我们还通过匹配渐近展开解析确定了基本$s$波的小质量准共振频率，并使用Leaver方法进行数值验证。与稳态处理不同，该计算保留了准束缚态的指数衰减。我们获得了度规微扰和Misner - Sharp质量的显式表达式，并推导了未来外俘获视界的演化。黑洞质量随衰减的视界通量单调增长，当有限标量云被吸收时饱和，在考虑的微扰阶数下，云质量的减少恰好平衡了视界的增长。我们还确定了标量小耦合近似和引力微扰展开同时有效的区域。
英文摘要
We analytically determine the leading backreaction of a spherically symmetric massive complex scalar quasi-bound state (with mass $μ$) on a Schwarzschild black hole with (initial) gravitational radius $r_0$. Working in the small-coupling regime, $r_0 μ\ll 1$, we evaluate the stress-energy tensor of the fundamental scalar $s$-wave and solve the Einstein equations through quadratic order in its amplitude in ingoing Eddington-Finkelstein coordinates. We also determine the small-mass quasi-resonant frequency of the fundamental $s$-wave analytically by matched asymptotic expansions and validate it numerically using Leaver's method. Unlike steady-state treatments, the calculation retains the exponential decay of the quasi-bound state. We obtain explicit expressions for the metric perturbations and Misner-Sharp mass and derive the evolution of the future outer trapping horizon. The black-hole mass grows monotonically with the decaying horizon flux and saturates when the finite scalar cloud has been absorbed, with the decrease of the cloud mass exactly balancing the horizon growth at the perturbative order considered. We also determine the domain in which the scalar small-coupling approximation and the gravitational perturbative expansion are simultaneously valid.
Comments24 pages, 5 figures
