论文标题
作为横向梯度的一系列扩展，广告中局部冲击的碰撞
Collision of localized shocks in AdS$_5$ as a series expansion in transverse gradients
论文作者
论文摘要
我们引入了一个计算框架，以更有效地计算五维渐近抗DE保姆空间中局部冲击的碰撞。我们在横向梯度中扩展了爱因斯坦方程，发现我们的数值结果与扩展中已经达到一阶的确切解决方案非常吻合。此外，在横向梯度中的一阶方程可以将其分解为两组微分方程。这些集合之一的整体场仅对边界可观察物的贡献可忽略不计，因此每次切片上的计算可以简化为几个平面冲击波方程的解决方案，以及每个横向平面“像素”的四个其他微分方程。以$ \ lyssim 10 \％$的误差为代价，在流体动物化时间和低至中期的误差中，有用的数值解决方案可以通过大约一个数量级加速。
We introduce a computational framework to more efficiently calculate the collision of localized shocks in five dimensional asymptotically Anti-de Sitter space. We expand the Einstein equations in transverse gradients and find that our numerical results agree well with exact solutions already at first order in the expansion. Moreover, the Einstein equations at first order in transverse gradients can be decoupled into two sets of differential equations. The bulk fields of one of these sets has only a negligible contribution to boundary observables, such that the computation on each time slice can be simplified to the solution of several planar shockwave equations plus four further differential equations for each transverse plane `pixel'. At the cost of errors of $\lesssim 10 \%$ at the hydrodynamization time and for low to mid rapidities, useful numerical solutions can be sped up by roughly one order of magnitude.
