Studies of Singularities, Black Holes, and Gravitational Radiation

这个项目将研究引力的两个方面：引力塌缩和引力辐射。当一个物体的引力强大到足以捕获光线时，这个物体就变成了一个黑洞。在黑洞内部，物体在自身引力的影响下继续变得越来越小，直到它变成一个具有无限密度和无限引力场的点，称为奇点。这个项目包括计算出引力崩塌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。正如无线电发射机中的电流产生无线电波一样，移动的质量产生引力波。物理学中最令人兴奋的最新发展之一是使用巨大的激光干涉仪作为探测器直接探测到这些引力波。引力辐射的一个有趣的方面是所谓的引力波记忆：即使在波过去之后，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，以及引力辐射的发射。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、引力波记忆和黑洞形成门槛处的临界行为的方法上。该项目将在类天奇点的方法中研究小尺度结构的形成。此外，还将对真空、渐近平坦时空的崩塌进行模拟，以验证在这种情况下形成强类空奇点和弱零奇点的猜想。在以前的工作中，这个小组发展了一种处理引力波记忆的方法，它使用微扰方法，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。这个项目将利用二阶微扰理论将这一方法扩展到处理引力辐射的记忆(Christodoulou记忆)。将对临界引力坍缩进行模拟，以更好地了解Choptuik临界解，特别是轻微超临界情况下视界内的结构，以及临界解在柯西视界附近的时空。爱因斯坦-以太理论将被研究，以确定它的一些黑洞解是否不稳定。此外，这一理论的初值公式将针对不对称的一般情况而开发。该奖项反映了NSF的法定使命，并已通过使用基金会的智力优势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: gravitational collapse and gravitational radiation. 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. 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 the formation of small scale structure in the approach to the generic spacelike singularity. In addition, simulations will be done of the collapse of vacuum, asymptotically flat spacetimes in order to test the conjecture that both strong spacelike singularities and weak null singularities form in this case. In previous work, this group 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 extend this approach to treat the memory of gravitational radiation (Christodoulou memory) using second order perturbation theory. Simulations will be performed of critical gravitational collapse to develop a better understanding of the Choptuik critical solution, in particular the structure inside the horizon of the slightly supercritical case, and the spacetime near the Cauchy horizon for the critical solution. Einstein-Aether theory will be studied to see whether some of its black hole solutions are unstable. In addition an initial value formulation of this theory will be developed for the general case of no symmetry.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.