标题： 关于尺度不变黑洞的稳定性 显示英文标题

标题： On the stability of scale-invariant black holes

摘要： 二次尺度不变引力非最小耦合到标量场提供了一个具有竞争力的暴胀模型，其特征是从不稳定固定点到稳定固定点的转变，这两个固定点都由常数标量场配置所表征。 我们在静态、球对称设置中对该模型进行了补充分析，得到了两个Schwarzschild-de Sitter解，这对应于宇宙学场景中存在的两个固定点。 从两个不同的角度彻底研究了这些解的稳定性。 首先，我们通过线性扰动分析在经典层面上研究该系统。 特别是，我们提供了扰动晚期行为的解析和数值结果，证明了这两个解的稳定和不稳定特性。 然后，我们基于欧几里得路径积分公式进行半经典、非线性分析。 通过研究在两个解上计算的欧几里得在壳作用量之间的差异，我们证明了不稳定的解具有亚稳特性，并且会自发地衰变为总是被偏好的稳定固定点。 显示英文摘要

摘要： Quadratic scale-invariant gravity non minimally coupled to a scalar field provides a competitive model for inflation, characterized by the transition from an unstable to a stable fixed point, both characterized by constant scalar field configurations. We provide a complementary analysis of the same model in the static, spherically symmetric setting, obtaining two Schwarzschild-de Sitter solutions, which corresponds to the two fixed points existing in the cosmological scenario. The stability of such solutions is thoroughly investigated from two different perspectives. First, we study the system at the classical level by the analysis of linear perturbations. In particular, we provide both analytical and numerical results for the late-time behavior of the perturbations, proving the stable and unstable character of the two solutions. Then we perform a semi-classical, non-linear analysis based on the Euclidean path integral formulation. By studying the difference between the Euclidean on-shell actions evaluated on both solutions, we prove that the unstable one has a meta-stable character and is spontaneously decaying into the stable fixed point which is always favoured.