Hyperbolic Geometry and Gravitational Waves

双曲几何和引力波

• 批准号: 2309084
• 负责人: Anil Zenginoglu
• 金额: $ 15万
• 依托单位: University of Maryland, College Park
• 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: https://www.nsf.gov/awardsearch/showAward?AWD_ID=2309084&HistoricalAwards=false
• 关键词: Hyperbolic; Geometry; Gravitational; Waves

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线几何形状计算重力波和黑洞扰动的能力。双曲线几何形状在几个科学领域，包括数学，物理学，生物学和机器学习。通过利用渐近双曲时表面的益处（称为倍重表面），我们可以有效地表示无限域中的传出波，从而使我们能够访问远离其源的重力波磁通量，并避免对有限计算网格的外部边界处理。该奖项将有助于更广泛地理解波传播与双曲线几何形状之间的相互作用，并为改善科学和工程中基本问题的解决方案提供了应用。此外，它将支持高度跨学科的学生的教育和培训，并通过外展努力，包括一所暑期传播的暑期学校来促进公共科学素养。折叠压实技术将无限领域映射到使用SCRI固定和彭罗斯压实的有限区域，从而将全球问题转化为当地问题。该技术显着有益于时空扰动和重力波的数值和分析处理。奖励活动将分为五个副标题，以调查具有不同重点和风险特征的倍曲面表面的应用。前三个子项目的重点是（i）扩大该方法在黑洞扰动理论中的应用范围，（ii）提供详细的数值分析，以及（iii）实施无界域中散射问题的倍曲面紧凑型。第四个子项目将尝试弯曲时间表面，以提高非线性爱因斯坦方程的现有代码的计算效率。第五个子项目将探索倍曲面表面在黑洞空间中的量子场的应用。该项目的潜在贡献包括改善时空扰动和重力波的数值和分析处理，为选择免费参数的选择提供了严格的准则，并为未来的研究打开了新的方向。该奖项反映了NSF的法规使命，并认为通过基金会的知识优点和广泛的critia criter scritia criter critia criter criteria criter critia criter critia criteria criter critia criteria criteria criteria criteria criteria criteria crietia rectiria均值得一评论。