Studies of Singularities, Black Holes, and Gravitational Radiation

本项目将研究重力的两个方面：(1)重力坍缩和(2)重力辐射。当一个物体的引力强大到足以捕获光时，这个物体就变成了黑洞。在黑洞内部，物体在自身引力的影响下继续变得越来越小，直到成为一个具有无限大密度和无限大引力场的点，称为奇点。这个项目包括计算在引力坍缩中形成的奇点的性质，特别是任何接近奇点的观察者所感受到的力。就像无线电发射机中的电流产生无线电波一样，运动的物体也会产生引力波。物理学中最近最令人兴奋的发展之一是使用巨大的激光干涉仪作为探测器直接探测这些引力波。引力波辐射的一个有趣的方面是引力波记忆：即使在引力波过去之后，引力波探测器也会发生永久性的变化。这个项目将研究这种引力波记忆的原因和性质。引力坍缩导致黑洞和时空奇点的形成，并发射引力辐射。这个项目将研究引力坍缩的所有这些方面，特别是将集中在奇点的方法，引力波记忆，以及黑洞形成阈值的临界行为。该项目将研究渐近平坦时空中的引力坍缩，以验证在这种情况下形成强类空间奇点和弱零奇点的猜想。先前的一个项目开发了一种处理引力波记忆的方法，该方法使用微扰方法，其中Weyl张量是基本变量，因此在一阶微扰理论中具有明显的规范不变性。本项目将使用这种方法来探索内存和波动方程属性之间的关系，并使用公开可用的模板库Weyl标量生成内存波形。此外，使用四分体方法的轴对称代码将被开发用于模拟临界引力坍缩和爱因斯坦以太理论。该奖项反映了美国国家科学基金会的法定使命，并通过使用基金会的知识价值和更广泛的影响审查标准进行评估，被认为值得支持。

This project will study two aspects of gravity: (1) gravitational collapse and (2) gravitational radiation. (1) When an object’s gravity becomes strong enough to trap light, the object becomes a black hole. Inside the black hole the object continues to become smaller and smaller under the influence of its own gravity until it becomes a point with infinite density and infinite gravitational field called a singularity. This project involves working out the properties of the singularities formed in gravitational collapse, and in particular the forces felt by any observer who approaches the singularity. (2) Just as the electric currents in a radio transmitter make radio waves, so moving masses make gravitational waves. One of the most exciting recent developments in physics is the direct detection of these gravitational waves using huge laser interferometers as the detectors. One interesting aspect of gravitational radiation is something called gravitational wave memory: even after the wave has passed, there is a permanent change in the gravitational wave detector. This project will study the causes and properties of this gravitational wave memory.Gravitational collapse results in the formation of black holes and spacetime singularities, and the emission of gravitational radiation. This project will study all of these aspects of gravitational collapse, and in particular will concentrate on the approach to the singularity, gravitational wave memory, and critical behavior at the threshold of black hole formation. The project will study gravitational collapse in asymptotically flat spacetimes in order to test the conjecture that both strong spacelike singularities and weak null singularities form in this case. A previous project developed a treatment of gravitational wave memory that uses a perturbative approach in which the Weyl tensor is the basic variable and thus has manifest gauge invariance in first order perturbation theory. This project will use this approach to explore the relation between memory and the properties of the wave equation, and to generate memory waveforms using publicly available template bank Weyl scalars. In addition, axisymmetric codes using tetrad methods will be developed to perform simulations of critical gravitational collapse and of Einstein-aether theory.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.