We explore systematically perturbations of self-similar solutions to the Einstein-axion-dilaton system, whose dynamics are invariant under spacetime dilations combined with internal 𝔰𝔩(2 , ℝ) transformations. The self-similar solutions capture the enticing behavior “critical” systems on the verge of gravitational collapse, in arbitrary spacetime dimensions. Our methods rest on a combination of analytical and numerical tools, apply to all three conjugacy classes of 𝔰𝔩(2 , ℝ) transformations and allow accurate estimates of the corresponding Choptuik exponents. It is well known that these exponents depend on the spacetime dimension and on the matter content. Our main result is that they also attain different values, even within a given conjugacy class, for the distinct types of critical solutions that we recently identified in the Einstein-axion-dilaton system.

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关于自相似坍塌的临界指数

我们系统地探索爱因斯坦-轴-膨胀系统的自相似解的扰动，其动力学在时空膨胀与内部 𝔰𝔩(2 , ℝ) 变换相结合的情况下是不变的。自相似解决方案在任意时空维度中捕获了处于引力坍缩边缘的诱人行为“关键”系统。我们的方法依赖于分析和数值工具的组合，适用于 𝔰𝔩(2 , ℝ) 变换的所有三个共轭类，并允许准确估计相应的 Choptuik 指数。众所周知，这些指数取决于时空维度和物质含量。我们的主要结果是它们也获得不同的值，即使在给定的共轭类中，