We investigate the impact of oscillations of a black hole's mass around its average value on the three-dimensional black hole geometry. Drawing on a classical framework that conceptualizes fluctuations near an event horizon as mass variations, we introduce a model where the metric of a black hole, formed from the collapse of a massive null shell, exhibits oscillatory behavior in spherical modes. This dynamic is encapsulated by a non-rotating BTZ-Vaidya solution, characterized by the black hole mass fluctuating at a resonant frequency ω and a small amplitude parameter μ0. Using a perturbative approach, solutions to the null geodesic equation are determined up to the second order in μ0. The temporal fluctuations of the event horizon's location induce alterations in the thermodynamic variables' values. Upon calculating the time-averaged values, the mean Hawking temperature experiences a slight decrease due to these fluctuations, while the mean entropy exhibits an increase. Furthermore, the study explores the influence of these fluctuations on the trajectories of null rays near the horizon, which ultimately reach the anti-de Sitter boundary at late times. The analytical computation of the general solution for the perturbed rays up to the second order underscores the novel approach of this study in examining the effects of mass oscillations on black hole thermodynamics and geometry, thereby contributing a unique perspective to the field.

中文翻译：

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非旋转 BTZ 黑洞中的质量涨落


我们研究了黑洞质量围绕其平均值的振荡对三维黑洞几何结构的影响。借鉴将事件视界附近的波动概念化为质量变化的经典框架，我们引入了一个模型，其中由大质量零壳塌缩形成的黑洞的度量在球形模式下表现出振荡行为。这种动态由非旋转 BTZ-Vaidya 解决方案封装，其特征是黑洞质量以共振频率 ω 和小振幅参数 μ0 波动。使用微扰方法，可以确定零测地方程的解，最高可达 μ0 的二阶。事件视界位置的时间波动会引起热力学变量值的变化。在计算时间平均值时，平均霍金温度由于这些波动而略有下降，而平均熵则有所增加。此外，该研究还探讨了这些涨落对地平线附近零射线轨迹的影响，这些轨迹最终最终到达反德西特边界。对二阶扰动射线通解的分析计算强调了本研究在检查质量振荡对黑洞热力学和几何形状的影响方面的新颖方法，从而为该领域提供了独特的视角。