论文标题
关于标尺不变的黑洞的稳定性
On the stability of scale-invariant black holes
论文作者
论文摘要
二次尺度不变的重力非微小耦合到标量场为通货膨胀提供了一个竞争模型，其特征是从不稳定到稳定的固定点的过渡，均以恒定标量场配置为特征。我们在静态的球形对称设置中提供了对同一模型的互补分析，获得了两个Schwarzschild-De Sitter Solutions，这与宇宙学场景中存在的两个固定点相对应。从两个不同的角度，对这种解决方案的稳定性进行了彻底研究。首先，我们通过线性扰动分析在经典级别研究系统。特别是，我们为扰动的晚期行为提供了分析和数值结果，证明了这两种溶液的稳定和不稳定特征。然后，我们基于欧几里得路径积分公式进行半古典的非线性分析。通过研究在两种溶液上评估的欧几里得在壳动作之间的差异，我们证明不稳定的溶液具有元稳定特征，并且自发地腐烂到稳定的固定点，这总是受到青睐的。
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.
