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给科学带来了革命性的变化，并为从GPS系统到移动的手机中的微芯片等日常小工具奠定了基础。然而，一个一致的量子引力理论仍然难以捉摸。对这样一个“万有理论”的追求通常会产生广义相对论的扩展，这些扩展会影响黑洞和中子星碰撞期间展开的强引力机制。LIGO获得诺贝尔奖的发现，在它们的螺旋和合并过程中发出的引力波开辟了新的发现渠道，以探索引力的本质。该奖项的主要目标是在最极端的非线性区域实现新的引力观测测试，从而促进NSF“宇宙之窗”大理念的科学进步。这项研究将与每年一次的国际“引力波日”的设立相结合。“这一系列更广泛的影响活动旨在向公众和高中生推广引力和引力波物理学的最新发现。该奖项支持超越弱场近似的超越广义相对论理论的适定时间演化公式的数学和计算发展。推导将适应最近的结果，在粘性流体力学和相对论的四维理论，这将是一个Cauchy问题与BSSN或Z4型重新制定和使用一个适应移动穿刺规。该奖项还支持PI的端到端，开源数值相对论框架Canuda的实施。它的设计高度模块化，因此，适应于一个大类的理论，使最大可能的发现空间。该奖项的第二部分侧重于在二次引力中对紧凑双星的广泛模拟，对其非线性动力学的研究，包括动态（去）标量化等新效应，以及在二次引力中构建数值引力波形。该奖项反映了NSF的法定使命，并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，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.