论文标题
关于自相似系统的扰动理论和关键指数
On Perturbation Theory and Critical Exponents for Self-Similar Systems
论文作者
论文摘要
已知爱因斯坦 - 轴 - 二元系统中的重力临界崩溃会导致连续的自相似解决方案，其特征是Choptuik临界指数$γ$。我们通过计算线性扰动方程来完成现有的文献，如果轴 - 迪拉顿系统采用抛物线形式。接下来，我们在双曲线的新发现的自相似解决方案中求解扰动方程，这使我们能够提取choptuik指数。我们的主要结果是，该指数不仅取决于时空的尺寸，还取决于特定的ANSATZ和一个人开始的关键解决方案。
Gravitational critical collapse in the Einstein-axion-dilaton system is known to lead to continuous self-similar solutions characterized by the Choptuik critical exponent $γ$. We complete the existing literature on the subject by computing the linear perturbation equations in the case where the axion-dilaton system assumes a parabolic form. Next, we solve the perturbation equations in a newly discovered self-similar solution in the hyperbolic case, which allows us to extract the Choptuik exponent. Our main result is that this exponent depends not only on the dimensions of spacetime but also the particular ansatz and the critical solutions that one started with.
