The Nonlinear Stability of Black Holes and the Structure of Spacetime Singularities in General Relativity
广义相对论中黑洞的非线性稳定性与时空奇点的结构
基本信息
- 批准号:1709270
- 负责人:
- 金额:$ 45.2万
- 依托单位:
- 依托单位国家:美国
- 项目类别:Continuing Grant
- 财政年份:2017
- 资助国家:美国
- 起止时间:2017-08-01 至 2020-07-31
- 项目状态:已结题
- 来源:
- 关键词:
项目摘要
This project strives to answer fundamental questions about black holes and the structure of spacetime. The research is a mathematical investigation of properties of solutions to Einstein's equations of general relativity that focuses on spacetime singularities. The project aims to advance rigorous mathematics to deepen understanding of the aspects of the physical world that are described by this remarkable theory of gravitation, which include the gravitational lensing of light from distant galaxies, the corrections to satellite clocks necessary for global positioning systems, and the gravitational waves observed from binary black hole collisions.This research aims to mathematically prove the nonlinear stability of black holes and answer fundamental questions concerning the nature of spacetime singularities in general relativity. The first major objective in this project is to provide a mathematical proof of the nonlinear stability conjecture for the Kerr metric. The other two major objectives of this research concern understanding the structure of various spacetimes with singularities. A series of projects will focus on showing that singularities do indeed exist in black holes, but they are not as "ferocious" as previously expected. Another class of spacetimes with singularities arise in analogy to a construction first done in the context of pure mathematics that has also attracted interest from theoretical physics. A second series of projects will concentrate on implementation of this construction in general relativity and analyze the precise nature of the resulting singularities.
这个项目致力于回答关于黑洞和时空结构的基本问题。这项研究是对爱因斯坦广义相对论方程解的性质的数学研究,其重点是时空奇点。该项目旨在推进严谨的数学,以加深对这一卓越的引力理论所描述的物理世界各个方面的理解,包括来自遥远星系的光的引力透镜,全球定位系统所需的卫星时钟的修正,以及从双黑洞碰撞中观察到的引力波。这项研究旨在从数学上证明黑洞的非线性稳定性,并回答广义相对论中有关时空奇点性质的基本问题。本项目的第一个主要目标是为克尔度量的非线性稳定性猜想提供数学证明。这项研究的另外两个主要目标是了解具有奇点的各种时空的结构。一系列项目将集中于证明黑洞中确实存在奇点,但它们并不像之前预期的那样“凶猛”。另一类具有奇点的时空的出现类似于最初在纯数学背景下完成的构造,也引起了理论物理学的兴趣。第二个系列项目将集中于在广义相对论中实现这一结构,并分析由此产生的奇点的精确性质。
项目成果
期刊论文数量(7)
专著数量(0)
科研奖励数量(0)
会议论文数量(0)
专利数量(0)
Uniform Boundedness and Continuity at the Cauchy Horizon for Linear Waves on Reissner–Nordström–AdS Black Holes
Reissner-Nordström-AdS 黑洞线性波柯西视界处的均匀有界性和连续性
- DOI:10.1007/s00220-019-03529-x
- 发表时间:2020
- 期刊:
- 影响因子:2.4
- 作者:Kehle, Christoph
- 通讯作者:Kehle, Christoph
The Asymptotically Self-Similar Regime for the Einstein Vacuum Equations
- DOI:10.1007/s00039-018-0448-9
- 发表时间:2017-05
- 期刊:
- 影响因子:2.2
- 作者:I. Rodnianski;Yakov Shlapentokh-Rothman
- 通讯作者:I. Rodnianski;Yakov Shlapentokh-Rothman
A Scattering Theory for Linear Waves on the Interior of Reissner–Nordström Black Holes
Reissner-Nordström 黑洞内部线性波的散射理论
- DOI:10.1007/s00023-019-00760-z
- 发表时间:2019
- 期刊:
- 影响因子:0
- 作者:Kehle, Christoph;Shlapentokh-Rothman, Yakov
- 通讯作者:Shlapentokh-Rothman, Yakov
The linear stability of the Schwarzschild solution to gravitational perturbations
- DOI:10.4310/acta.2019.v222.n1.a1
- 发表时间:2019-01-01
- 期刊:
- 影响因子:3.7
- 作者:Dafermos, Mihalis;Holzegel, Gustav;Rodnianski, Igor
- 通讯作者:Rodnianski, Igor
A proof of the instability of AdS for the Einstein-null dust system with an inner mirror
- DOI:10.2140/apde.2020.13.1671
- 发表时间:2017-04
- 期刊:
- 影响因子:2.2
- 作者:Georgios Moschidis
- 通讯作者:Georgios Moschidis
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Igor Rodnianski其他文献
A physical space approach to wave equation bilinear estimates
- DOI:
10.1007/bf02868479 - 发表时间:
2002-12-01 - 期刊:
- 影响因子:0.900
- 作者:
Sergiu Klainerman;Igor Rodnianski;Terence Tao - 通讯作者:
Terence Tao
OF RADIATION FIELDS OF FREE WAVES
自由波的辐射场
- DOI:
- 发表时间:
- 期刊:
- 影响因子:0
- 作者:
I. Liangl;R. U. S. Hen;EI Lijuanw;Vadim Kaloshin;A. Mazzucato;Richard B. Melrose Massachussets;Frank Merle;Werner Müller;Igor Rodnianski;Terence Tao;Michael E. Taylor;Dan Virgil;J. Wright - 通讯作者:
J. Wright
ON L ∞ ESTIMATES FOR MONGE–AMPÈRE AND HESSIAN EQUATIONS
蒙日-安培方程和黑森方程的 L ∞ 估计
- DOI:
- 发表时间:
- 期刊:
- 影响因子:0
- 作者:
UO Bing;F. R. D UONG H. P HONG;C. H. W. Ang;Vadim Kaloshin;A. Mazzucato;Richard B. Melrose Massachussets;Frank Merle;Werner Müller;Igor Rodnianski;Terence Tao;Michael E. Taylor;Dan Virgil;J. Wright - 通讯作者:
J. Wright
WITH WHITE NOISE POTENTIAL ON COMPACT SURFACES
紧凑表面上可能存在白噪声
- DOI:
- 发表时间:
- 期刊:
- 影响因子:0
- 作者:
A. N. M. Ouzard;I. M. Z. Achhuber;Vadim Kaloshin;A. Mazzucato;Richard B. Melrose Massachussets;Frank Merle;Werner Müller;Igor Rodnianski;Terence Tao;Michael E. Taylor;Dan Virgil;J. Wright - 通讯作者:
J. Wright
QUANTITATIVE ALEXANDROV
定量亚历山德罗夫
- DOI:
- 发表时间:
- 期刊:
- 影响因子:0
- 作者:
V. E. J. Ulin;J. O. N. Iinikoski;Patrick Gérard;A. Mazzucato;Richard B. Melrose Massachussets;Frank Merle;Werner Müller;Igor Rodnianski;Terence Tao;Michael E. Taylor;Dan Virgil;J. Wright - 通讯作者:
J. Wright
Igor Rodnianski的其他文献
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{{ truncateString('Igor Rodnianski', 18)}}的其他基金
Beyond Stability of Black Holes in General Relativity
超越广义相对论中黑洞的稳定性
- 批准号:
2005464 - 财政年份:2020
- 资助金额:
$ 45.2万 - 项目类别:
Continuing Grant
Singularities and Black Holes in General Relativity
广义相对论中的奇点和黑洞
- 批准号:
1900288 - 财政年份:2019
- 资助金额:
$ 45.2万 - 项目类别:
Continuing Grant
General Relativity and geometric hypersolic PDEs
广义相对论和几何超音速偏微分方程
- 批准号:
1001500 - 财政年份:2010
- 资助金额:
$ 45.2万 - 项目类别:
Continuing Grant
General Relativity and Geometric Hyperbolic PDEs
广义相对论和几何双曲偏微分方程
- 批准号:
0702270 - 财政年份:2007
- 资助金额:
$ 45.2万 - 项目类别:
Continuing Grant
Local Regularity and Long Time Behavior of Solutions on Non-Linear Evolution Equations
非线性演化方程解的局部正则性和长期行为
- 批准号:
0406627 - 财政年份:2004
- 资助金额:
$ 45.2万 - 项目类别:
Standard Grant
Regularity and Dispersive Properties of Evolution Equations
演化方程的正则性和色散性质
- 批准号:
0107791 - 财政年份:2001
- 资助金额:
$ 45.2万 - 项目类别:
Continuing Grant
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随机激励下多稳态系统的临界过渡识别及Basin Stability分析
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- 资助金额:65.0 万元
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Stability of Black Holes and the Nature of Singularities in General Relativity
广义相对论中黑洞的稳定性和奇点的性质
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