Studies of Singularities, Black Holes, and Gravitational Radiation

本项目将研究重力的两个方面：重力坍缩和重力辐射。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，移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。该项目将研究一般类空间奇点方法中小尺度结构的形成。此外，还将对真空、渐近平坦时空的坍缩进行模拟，以验证在这种情况下会形成强类空间奇点和弱零奇点的猜想。在之前的工作中，该小组开发了一种使用微扰方法处理引力波记忆的方法，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。本项目将扩展这一方法，利用二阶摄动理论来处理引力辐射的记忆（Christodoulou记忆）。为了更好地理解Choptuik临界解，特别是轻微超临界情况下视界内的结构，以及临界解的柯西视界附近的时空，将进行临界引力坍缩的模拟。人们将研究爱因斯坦以太理论，看看它的一些黑洞解是否不稳定。此外，对于一般情况下的无对称性，将发展出这个理论的初始值公式。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: 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.