Analysis of extremal black holes
极值黑洞分析
基本信息
- 批准号:1265538
- 负责人:
- 金额:$ 14.8万
- 依托单位:
- 依托单位国家:美国
- 项目类别:Continuing Grant
- 财政年份:2013
- 资助国家:美国
- 起止时间:2013-08-01 至 2016-07-31
- 项目状态:已结题
- 来源:
- 关键词:
项目摘要
This project concerns the investigation of two of the most outstanding conjectures in general relativity, namely the uniqueness and stability of the Kerr family of black holes, by concentrating on the special class of extremal black holes. Recent contributions of the PI showed that waves exhibit instability properties along the event horizon originating from a novel hierarchy of conservation laws. Moreover, extremal black holes exhibit very strong trapping which is coupled with the above conservation laws and also the phenomenon of superradiance (i.e. the extraction of energy from the black hole). Satisfactory techniques have been developed to overcome the problem of trapping in the non-extremal case; however, in view of the aforementioned geometric couplings, these methods break down in the extremal case. The PI expects that this project will develop the necessary tools and techniques to provide a rigorous and definitive understanding of evolution equations on such spacetimes. In particular, the PI intends to continue the rigorous study of linear and nonlinear waves and investigate the distribution of quasinormal modes on such backgrounds. The PI will also work on the global existence and breakdown criteria for quasilinear equations on extremal Kerr hoping to gain insights for the ultimate goal of this proposal, namely the fully non-linear stability and instability and uniqueness problem for extremal black holes. General relativity is the classical theory that describes the evolution of physical systems under the effect of gravity. One of the most celebrated predictions of the theory is the existence of so-called black hole regions, i.e. regions from where light cannot escape to infinity. Not only have these regions captured the imagination of scientists, but have also found profound applications to astronomy, physics, and mathematics. A particularly important class of black holes consists of the so-called extremal black holes, that is black holes with zero temperature. The latter are central objects of study in the high-energy physics community. The PI has initiated a rigorous mathematical study of evolution equations on such spacetimes and interesting and surprising results have emerged. Specifically, a novel instability has been discovered on the event horizon of extremal black holes bearing a wide range of potential applications regarding the mathematics and physics of black holes. Specialists in high-energy physics and numerical relativity are further researching the applications of this instability in other contexts. The PI expects that this project will unravel the complex interaction between the analysis, geometry and physics of extremal black holes. Moreover, the PI intends to start new collaborations which will lead to exchange of knowledge and also increase interactions with members of the physics, numerical relativity and astrophysics community. The PI plans to teach seminars at various places aiming at introducing students and researchers to the very rich mathematical structure of general relativity.
这个项目涉及广义相对论中两个最杰出的命题的研究,即克尔族黑洞的唯一性和稳定性,通过集中在特殊的极端黑洞类。PI最近的贡献表明,波表现出不稳定性特性沿着事件视界起源于一个新的层次的守恒定律。此外,极端黑洞表现出非常强的捕获,这与上述守恒定律和超辐射现象(即从黑洞中提取能量)相结合。已经开发出令人满意的技术来克服在非极值情况下的捕获问题;然而,鉴于上述几何耦合,这些方法在极值情况下失效。PI希望该项目将开发必要的工具和技术,以提供对此类时空演化方程的严格和明确的理解。特别是,PI打算继续对线性和非线性波进行严格的研究,并调查在这种背景下准正规模式的分布。PI还将致力于极值Kerr上准线性方程的全局存在性和崩溃准则,希望能够深入了解该提案的最终目标,即极值黑洞的完全非线性稳定性和不稳定性以及唯一性问题。广义相对论是描述物理系统在重力作用下演化的经典理论。该理论最著名的预测之一是所谓的黑洞区域的存在,即光不能逃逸到无限远的区域。这些区域不仅激发了科学家的想象力,而且在天文学、物理学和数学方面也有着深远的应用。一类特别重要的黑洞是所谓的极端黑洞,即温度为零的黑洞。后者是高能物理界研究的中心对象。PI发起了一项严格的数学研究,对这种时空的演化方程进行了研究,并出现了有趣和令人惊讶的结果。具体来说,一种新的不稳定性已被发现的极端黑洞的事件视界轴承广泛的潜在应用有关的黑洞的数学和物理。高能物理和数值相对论的专家正在进一步研究这种不稳定性在其他背景下的应用。PI预计,该项目将揭示极端黑洞的分析,几何和物理之间的复杂相互作用。此外,PI打算开始新的合作,这将导致知识交流,并增加与物理学,数值相对论和天体物理学社区成员的互动。PI计划在不同的地方举办研讨会,旨在向学生和研究人员介绍广义相对论非常丰富的数学结构。
项目成果
期刊论文数量(0)
专著数量(0)
科研奖励数量(0)
会议论文数量(0)
专利数量(0)
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Stefanos Aretakis其他文献
The Characteristic Gluing Problem for the Einstein Vacuum Equations: Linear and Nonlinear Analysis
- DOI:
10.1007/s00023-023-01394-y - 发表时间:
2023-12-07 - 期刊:
- 影响因子:1.300
- 作者:
Stefanos Aretakis;Stefan Czimek;Igor Rodnianski - 通讯作者:
Igor Rodnianski
Stefanos Aretakis的其他文献
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{{ truncateString('Stefanos Aretakis', 18)}}的其他基金
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