论文标题
在4+1维度中，重力塌陷中的临界现象与竞争标量场和重力波
Critical phenomena in gravitational collapse with competing scalar field and gravitational waves, in 4+1 dimensions
论文作者
论文摘要
在球形对称性以外的物质的重力崩溃中，重力波必定存在。另一方面，即使没有物质，重力波也会崩溃到黑洞。因此，人们可能会想知道物质场和重力波之间的相互作用和竞争如何影响黑洞形成阈值的临界现象。作为此的玩具模型，我们研究了4+1个维度的黑洞形成的阈值，在这里，我们在Bizón，Chmaj和Schmidt的引力浪潮Ansatz中添加了无质量的微型耦合标量物质字段（在$ s^3 \ s^3 \ s^3 \ times \ time nime nime nime n Nutshell，bianchi in n nutshell，bianchi phime} nime timie pextipe {为了找到在4+1个物理维度中管理重力波的方程式的稳定离散化，该方程与9+1个维度的球形波方程具有相同的主要部分，我们首先回顾了与大$ n $ n $ n $ n $ n $ n $ n $ n $ n $ n $ n $ n $ n $ n $ n $ n $ n $ n $ n $ n $ n $ n $ n $ n $ n $ n $ n $ n $。回到主要问题，我们从数值上发现标量场临界溶液衰减的弱重力波扰动，而重力波临界溶液的弱标量扰动也衰减。然后，动态系统的图像表明存在编码两个吸引子。我们通过进化混合的初始数据并微调整体振幅和两个磁场的相对强度来找到该吸引子的数值证据。
In the gravitational collapse of matter beyond spherical symmetry, gravitational waves are necessarily present. On the other hand, gravitational waves can collapse to a black hole even without matter. One might therefore wonder how the interaction and competition between the matter fields and gravitational waves affects critical phenomena at the threshold of black hole formation. As a toy model for this, we study the threshold of black-hole formation in 4+1 dimensions, where we add a massless minimally coupled scalar matter field to the gravitational wave ansatz of Bizón, Chmaj and Schmidt (in a nutshell, Bianchi~IX on $S^3\times\text{radius}\times\text{time}$). In order to find a stable discretisation of the equation governing the gravitational waves in 4+1 physical dimensions, which has the same principal part as the spherical wave equation in 9+1 dimensions, we first revisit the problem of critical spherical scalar field collapse in $n+2$ dimensions with large $n$. Returning to the main problem, we find numerically that weak gravitational wave perturbations of the scalar field critical solution decay, while weak scalar perturbations of the gravitational wave critical solution also decay. A dynamical systems picture then suggests the existence of a codimension-two attractor. We find numerical evidence for this attractor by evolving mixed initial data and fine-tuning both an overall amplitude and the relative strength of the two fields.
