论文标题
共振动力和盒子Minkowski模型的不稳定性
Resonant Dynamics and the Instability of the Box Minkowski Model
论文作者
论文摘要
我们重新访问盒子Minkowski模型[Phys。莱特牧师。 109，221101（2012）]并提供了一个强有力的论点，即遵守Dirichlet边界条件，它不稳定，对于任意小的通用扰动而言，它是不稳定的。使用弱非线性扰动理论，我们得出了共振系统，该系统与具有抗DE保姆渐近器的系统相比具有额外的谐振术语，并研究了其特性，包括保守量。我们发现，在有限的时间内，共振系统的通用解决方案变得奇异。令人惊讶的是，附加的共振相互作用不会显着影响奇异演化。此外，我们发现相互作用系数采用相对简单的形式，使其成为湍流引力不稳定性的特别有吸引力的玩具模型。
We revisit the box Minkowski model [Phys. Rev. Lett. 109, 221101 (2012)] and provide a strong argument that, subject to the Dirichlet boundary condition, it is unstable toward black hole formation for arbitrarily small generic perturbations. Using weakly nonlinear perturbation theory, we derive the resonant system, which compared to systems with the anti-de Sitter asymptotics, has extra resonant terms, and study its properties, including conserved quantities. We find that the generic solution of the resonant system becomes singular in finite time. Surprisingly, the additional resonant interactions do not significantly affect the singular evolution. Furthermore, we find that the interaction coefficients take a relatively simple form, making this a particularly attractive toy model of turbulent gravitational instability.
