Singularities and Black Holes in General Relativity

广义相对论中的奇点和黑洞

• 批准号: 1900288
• 负责人: Igor Rodnianski
• 金额: $ 19.02万
• 依托单位: Princeton University
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2019
• 资助国家: 美国
• 起止时间: 2019-07-01 至 2023-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1900288&HistoricalAwards=false
• 关键词: Singularities; Black; Holes; General; Relativity

One of the most shocking predictions of general relativity is the existence of black holes; regions of spacetime so dense that nothing, not even light, can escape. In addition to possessing fascinating physical properties, black holes play an essential role in our modern understanding of astrophysics. For example, it is expected that any object undergoing gravitational collapse eventually settles down to a black hole, and also, it is thought that black holes serve to shield us from potentially dangerous gravitational singularities. However, both of these expectations, so fundamental to our view of the universe, lack a definitive mathematical understanding. This project aims to advance our understanding of both the problems of black hole stability and the potential existence of "naked singularities", singular solutions which are not hidden away behind a black hole.In the last decade there has been a tremendous progress in establishing stability results for model equations on general black hole backgrounds. At the same time, there has been much progress in understanding the true stability problem for the special class of non-rotating black holes. One part of our research plan is to combine these two research directions and to eventually establish a definitive stability theory for rotating black holes. Another part of our research plan is to show that there do in fact exist singular spacetimes which are not hidden behind black holes; however, we will also show that upon a slight perturbation, these particular spacetimes become unstable and develop a black hole.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.

广义相对论最令人震惊的预言之一是黑洞的存在;时空区域如此密集，以至于任何东西，甚至光，都无法逃脱。除了拥有迷人的物理特性外，黑洞在我们对天体物理学的现代理解中发挥着重要作用。例如，任何经历引力坍缩的物体最终都会沉降为黑洞，而且，人们认为黑洞可以保护我们免受潜在危险的引力奇点的影响。然而，这两种对我们宇宙观至关重要的期望，都缺乏明确的数学理解。这个项目的目的是提高我们对黑洞稳定性问题和“裸奇点”潜在存在性的认识，裸奇点是指没有隐藏在黑洞后面的奇异解。在过去的十年里，在建立一般黑洞背景下模型方程的稳定性结果方面取得了巨大的进展。与此同时，在理解这类特殊的非旋转黑洞的真正稳定性问题方面也取得了很大进展。我们的研究计划之一是将这两个研究方向联合收割机，最终建立一个确定的旋转黑洞稳定性理论。我们的研究计划的另一部分是证明确实存在奇异时空，它们并不隐藏在黑洞后面;然而，我们也将证明，在轻微的扰动下，这些特定的时空变得不稳定并发展成黑洞。这个奖项反映了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。

项目成果

Naked singularities for the Einstein vacuum equations: The exterior solution

• DOI: 10.4007/annals.2023.198.1.3
• 发表时间: 2019-12
• 期刊: Annals of Mathematics
• 影响因子: 4.9
• 作者: I. Rodnianski;Yakov Shlapentokh-Rothman

A Scattering Theory Approach to Cauchy Horizon Instability and Applications to Mass Inflation

柯西视界不稳定性的散射理论方法及其在大规模通货膨胀中的应用

• DOI: 10.1007/s00023-022-01216-7
• 发表时间: 2023
• 期刊: Annales Henri Poincaré
• 作者: Luk, Jonathan;Oh, Sung-Jin;Shlapentokh-Rothman, Yakov
• 通讯作者: Shlapentokh-Rothman, Yakov

Twisted Self-Similarity and the Einstein Vacuum Equations

扭曲自相似性和爱因斯坦真空方程

• 发表时间: 2023
• 期刊: Communications in mathematical physics
• 影响因子: 2.4
• 作者: Rothman-Slapentokh, Yakov