CAREER: Exploring the Photon Ring and Broadening Participation in Relativity via Interactive Black Hole Visualizations

在过去的几年里，NSF的激光干涉引力波天文台（LIGO）探测到了黑洞合并发出的第一个引力波，NSF支持的事件视界望远镜（EHT）捕获了第一个天体物理黑洞的电磁图像。在接下来的20年里，这些引力波和射电干涉仪的未来扩展预计将提供两个看似不同（但实际上，密切相关）的现象越来越精确的观测：围绕超大质量黑洞运行的光的“光子环”，以及合并后黑洞的后期准正常模式“振铃”。在这个项目中，范德比尔特大学的一个研究小组将阐明这两种看似不同的现象之间的理论联系，并为下一代计划中的引力实验做出新的预测。与此同时，该团队还将开发一个开源的交互式视觉展览，展示黑洞透镜效应，并将在LIGO的科学教育中心展出。虽然黑洞图像中的光子环和引力波形中的准正规模衰荡乍看起来是完全不同的现象，但实际上它们在高频程函极限中是密切相关的：在这种情况下，无质量场的波（如电磁波或引力波）可以由测地线的零同余构成，在所谓的几何光学近似下，黑洞的准正规模精确地对应于几乎束缚的光子轨道，其图像形成了它的光子环。由该奖项资助的团队将完善和扩展这种理论联系，将利用它来分析研究克尔黑洞的准正常模式，并揭示其光谱不稳定性，并将利用它来探索支配光子环及其相关准正常模式光谱的涌现共形对称性。在平行的研究中，该团队还将阐明黑洞图像如何在光子环和偏振近视界发射中编码自旋信息，然后将识别从黑洞自旋能量中提取电磁能量的尖锐特征。该奖项反映了NSF的法定使命，并通过使用基金会的智力价值和更广泛的影响审查标准进行评估，被认为值得支持。

In the last few years, NSF's Laser Interferometer Gravitational-Wave Observatory (LIGO) detected the first gravitational waves emitted from a black-hole merger, and the NSF-supported Event Horizon Telescope (EHT) has captured the first electromagnetic images of an astrophysical black hole. Over the next two decades, future extensions of these gravitational-wave and radio interferometers are expected to deliver increasingly precise observations of two seemingly disparate (but in reality, deeply connected) phenomena: the “photon ring” of light that orbited around a supermassive black hole, and the late-time quasinormal-mode “ringdown” of a post-merger black hole. During this project, a team of researchers based at Vanderbilt University will elucidate the theoretical connections between these two seemingly disparate phenomena and produce new predictions for the next generation of planned gravitational experiments. At the same time, this team will develop an open-source interactive visual exhibit that illustrates black hole lensing, to be displayed at LIGO’s Science Education Centers.Although the photon ring in black hole images and the quasinormal-mode ringdown in gravitational waveforms may at first sight appear to be entirely different phenomena, they are in fact closely related in the eikonal limit of high frequency: in that regime, waves of massless fields (such as electromagnetic or gravitational waves) can be constructed out of null congruences of geodesics, and under the so-called geometric optics approximation, the quasinormal modes of a black hole correspond precisely to the nearly bound photon orbits whose images form its photon ring. The team funded by this award will refine and extend this theoretical connection, will exploit it to analytically study the quasinormal modes of a Kerr black hole and shed light on their spectral instability, and will use it to explore an emergent conformal symmetry that governs the photon ring and its associated quasinormal-mode spectrum. In a parallel line of research, this team will also elucidate how black hole images encode spin information within the photon ring and in polarized near-horizon emission and will then identify sharp signatures of electromagnetic energy extraction from a black hole’s spin energy.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.