Hyperbolic Geometry and Gravitational Waves
双曲几何和引力波
基本信息
- 批准号:2309084
- 负责人:
- 金额:$ 15万
- 依托单位:
- 依托单位国家:美国
- 项目类别:Continuing Grant
- 财政年份:2023
- 资助国家:美国
- 起止时间:2023-05-01 至 2026-04-30
- 项目状态:未结题
- 来源:
- 关键词:
项目摘要
This award aims to improve the ability to compute gravitational waves and black hole perturbations using hyperbolic geometry. Hyperbolic geometry plays a crucial role in several scientific fields, including mathematics, physics, biology, and machine learning. By exploiting the benefits of asymptotically hyperbolic time surfaces, called hyperboloidal surfaces, we can efficiently represent outgoing waves in an infinite domain, allowing us to access the gravitational wave flux far away from its sources and avoid the outer boundary treatment of finite computational grids. This award will contribute to the broader understanding of the interactions between wave propagation and hyperbolic geometry and provide applications to improve the solution of fundamental problems in science and engineering. Additionally, it will support the education and training of a highly interdisciplinary student and promote public scientific literacy through outreach efforts, including a summer school on wave propagation.The hyperboloidal compactification technique maps infinite domains to finite regions using scri-fixing and Penrose compactification, thereby translating global problems into local ones. This technique significantly benefits the numerical and analytical treatment of spacetime perturbations and gravitational waves. The award activity will be divided into five subprojects to investigate the applications of hyperboloidal surfaces with different focuses and risk profiles. The first three subprojects focus on (i) broadening the range of applications of the method in black hole perturbation theory, (ii) providing detailed numerical analysis, and (iii) implementing hyperboloidal compactification for scattering problems in unbounded domains. The fourth subproject will experiment with bending up time surfaces to improve the computational efficiency of existing codes for nonlinear Einstein equations. The fifth subproject will explore the application of hyperboloidal surfaces to quantum fields in black hole spacetimes. The potential contributions of the project include improving the numerical and analytical treatment of spacetime perturbations and gravitational waves, providing rigorous guidelines for the choices of free parameters, and opening up new directions for future research.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.
该奖项旨在提高使用双曲几何计算引力波和黑洞扰动的能力。双曲几何在数学、物理学、生物学和机器学习等多个科学领域中发挥着至关重要的作用。通过利用渐进双曲时间表面(称为双曲面)的优点,我们可以有效地表示无限域中的传出波,使我们能够访问远离其源的引力波通量,并避免有限计算网格的外边界处理。该奖项将有助于更广泛地理解波传播和双曲几何之间的相互作用,并提供应用程序,以改善科学和工程中的基本问题的解决方案。此外,它还将支持教育和培训高度跨学科的学生,并通过外联努力,包括举办波传播暑期班,提高公众的科学素养双曲面紧致化技术使用scri-fixing和Penrose紧致化将无限域映射到有限区域,从而将全球问题转化为局部问题。这种方法对时空微扰和引力波的数值和分析处理有很大的好处。该奖项活动将分为五个子项目,以研究具有不同重点和风险特征的双曲面的应用。前三个子项目的重点是(i)扩大黑洞微扰理论的方法的应用范围,(ii)提供详细的数值分析,(iii)实现无界域散射问题的双曲面紧化。第四个子项目将试验弯曲时间表面,以提高非线性爱因斯坦方程现有代码的计算效率。第五个子项目将探讨双曲面在黑洞时空量子场中的应用。该项目的潜在贡献包括改进时空扰动和引力波的数值和分析处理,为自由参数的选择提供严格的指导方针,并为未来的研究开辟新的方向。该奖项反映了NSF的法定使命,并被认为值得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来支持。
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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Anil Zenginoglu其他文献
Data Science Education in Undergraduate Physics: Lessons Learned from a Community of Practice
本科物理中的数据科学教育:从实践社区中汲取的经验教训
- DOI:
- 发表时间:
2024 - 期刊:
- 影响因子:0
- 作者:
Karan Shah;Julie Butler;Alexis Knaub;Anil Zenginoglu;William Ratcliff;Mohammad Soltanieh - 通讯作者:
Mohammad Soltanieh
Hyperboloidal foliations with scri-fixing in spherical symmetry
具有球对称划线固定的双曲面叶状结构
- DOI:
10.1142/9789812834300_0213 - 发表时间:
2006 - 期刊:
- 影响因子:0
- 作者:
Anil Zenginoglu;S. Husa - 通讯作者:
S. Husa
Symmetric integration of the 1+1 Teukolsky equation on hyperboloidal foliations of Kerr spacetimes
克尔时空双曲面叶状结构上 1 1 Teukolsky 方程的对称积分
- DOI:
- 发表时间:
2023 - 期刊:
- 影响因子:0
- 作者:
C. Markakis;Sean Bray;Anil Zenginoglu - 通讯作者:
Anil Zenginoglu
A null infinity layer for wave scattering
- DOI:
- 发表时间:
2021-11 - 期刊:
- 影响因子:0
- 作者:
Anil Zenginoglu - 通讯作者:
Anil Zenginoglu
Numerical calculations near spatial infinity
空间无穷大附近的数值计算
- DOI:
10.1088/1742-6596/66/1/012027 - 发表时间:
2006 - 期刊:
- 影响因子:0
- 作者:
Anil Zenginoglu - 通讯作者:
Anil Zenginoglu
Anil Zenginoglu的其他文献
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