In this contribution we present an overview of our work on the numerical simulation of the perturbation of a black hole space-time by incoming gravitational waves. The formulation we use is based on Friedrich’s general conformal equations which have the unique property that they allow access to the asymptotic region of an asymptotically regular space-time. In our approach we set up an initial boundary value problem on a finite boundary, which cleanly separates the initial conditions, a static black hole, from the perturbation, an incoming gravitational wave specified by a spin-2 function on the time-like boundary. The main advantage of this approach is that the finite boundary expands fast enough to reach null-infinity where the asymptotic properties can be studied. This provides, for the first time, a direct relationship between finite initial and boundary data and asymptotic quantities within one simulation. We discuss the possibilities and limitations of this approach.

在这篇文章中，我们概述了我们对入射引力波对黑洞时空扰动的数值模拟工作。我们使用的公式基于弗里德里希的一般共形方程，这些方程具有独特的性质，即它们允许访问渐近规则时空的渐近区域。在我们的方法中，我们在有限边界上设置了一个初始边界值问题，它清楚地将初始条件（静态黑洞）与扰动（由自旋 2 函数在类时间边界上指定的入射引力波）分开。这种方法的主要优点是有限边界扩展得足够快，可以达到零无穷大，在那里可以研究渐近性质。这首次在一个模拟中提供了有限初始和边界数据与渐近量之间的直接关系。我们将讨论这种方法的可能性和局限性。