Numerical Relativity Framework for Strong-Field Tests of Gravity

广义相对论和量子物理学在上个世纪彻底改变了科学，并为从全球定位系统到手机中的微芯片等日常设备奠定了基础。然而，一个一致的量子引力理论仍然难以捉摸。对这种“万有理论”的探索通常会产生广义相对论的延伸，影响黑洞和中子星碰撞过程中展开的强引力体系。获得诺贝尔奖的LIGO发现了引力波在激发和合并过程中发出的引力波，这为探索引力的本质开辟了新的发现渠道。该奖项的主要目标是在最极端的非线性状态下对引力进行新的观测测试，从而促进美国国家科学基金会“宇宙之窗”大构想的科学进展。这项研究将与设立一年一度的国际“引力波日”相结合。这一系列影响广泛的活动旨在向普通大众和高中生推广重力和引力波物理学的最新发现。该奖项支持在数学和计算方面对超越广义相对论理论、超越弱场近似的适定时间演化公式的发展。该推导将采用粘性流体力学和四维理论的相对论的最新结果，这将被视为具有BSSN或Z4型重新表述并使用适应的移动穿刺计的柯西问题。该奖项进一步支持PI端到端的开源数值相对论框架Canuda的实现。它的设计是高度模块化的，因此，可以适应大量的理论，以实现最大可能的发现空间。该奖项的第二部分侧重于二次重力下紧双星的广泛模拟，对其非线性动力学的研究，包括动态（去）标化等新效应，以及二次重力下数值重力波形的构建。该奖项反映了美国国家科学基金会的法定使命，并通过使用基金会的知识价值和更广泛的影响审查标准进行评估，被认为值得支持。

General relativity and quantum physics have revolutionized science in the last century, and laid the foundations for every-day gadgets from the GPS systems to the microchips in our mobile phones. Yet, a consistent theory of quantum gravity has remained elusive. The quest for a such a "theory of everything" typically yields extensions of general relativity that impact the strong gravity regime unfolding during the collision of black holes and neutron stars. LIGO's Nobel-prize winning discoveries of gravitational waves emitted during their inspiral and merger have opened new discovery channels to probe the very nature of gravity. The key objective of this award is to enable new observational tests of gravity in its most extreme, nonlinear regime and thus promote the progress of science of NSF's "Windows on the Universe" Big Idea. The research will be integrated with the creation of an annual, international "Gravitational Wave Day." This series of broader impact activities aims at promoting the latest discovery in Gravity and Gravitational Wave physics to the general public as well as high-school students.This award supports the mathematical and computational development of well-posed time evolution formulations of beyond-GR theories, beyond the weak field approximation, for numerical relativity. The derivation will adapt recent results in viscous hydrodynamics and relativity for the four-dimensional theory, which will be cast as a Cauchy problem with a BSSN or Z4 type reformulation and using an adapted moving puncture gauge. The award furthermore supports the implementation in the PI's end-to-end, open-source numerical relativity framework Canuda. It is designed highly modular and, thus, adaptable to a large class of theories to enable the largest possible discovery space. The second part of the award focuses on extensive simulations of compact binaries in quadratic gravity, the investigation of their nonlinear dynamics, including new effects like dynamical (de-) scalarization, and the construction of numerical gravitational waveforms in quadratic gravity.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.