Quantum Gravity, Horizons, and Beyond

该基金将支持引力物理学几个方面的研究项目，其中弯曲时空起着关键作用。其中一组主题涉及理解时空的量子性质这一突出的基本问题。具体来说，研究将根据时空量子态的性质进行。大部分工作都集中在事件视界的特殊作用上，因为它被认为是揭开量子引力之谜的一个有希望的窗口。其他工作将通过探索爱因斯坦引力理论的某些修正的理论和观测结果，特别是对黑洞行为的影响，来探测爱因斯坦引力理论的有效性。该研究的另一个组成部分将解决有关天体物理体（如中子星和黑洞）周围磁化等离子体的行为问题，同时考虑到弯曲时空的影响。这项工作有助于更好地理解用射电望远镜对这些天体及其周围环境的观测。最后，与一个实验原子量子流体研究小组合作，研究方向将是探索和利用量子流体与弯曲时空（如膨胀的宇宙）中的场的物理类比。拟议的研究结果将通过书面文章、研讨会、会议演讲和座谈会传播，并将有助于我们对基本问题的理解，以及以更跨学科的方式进行观察和实验。PI将为研究生和本科生提供科学研究、写作和口头交流方面的指导和指导。PI将在马里兰大学的暑期课程中设计和实施针对即将升学的九年级学生和对物理感兴趣的高中女生的教学。所有这些活动都将有助于技术培训和科学素养，以及理解和欣赏物理学的见解。主要研究领域包括：1)计算量子引力系综视界熵的路径积分方法，2)2+1维引力中紧致域的非微扰约化相空间量子化，3)出射黑洞模式的起源，4)玻色-爱因斯坦凝聚中的模拟量子场论，5)黑洞和中子星周围磁螺旋度的广义相对论处理，以及6)违反洛伦兹引力理论中的黑洞视界。在1)项下，一个项目将研究非微扰路径积分方法与最近使用代数量子场论进行的半经典分析之间的关系，另一个项目将探讨近视界虚时间演化方法在计算视界熵时的作用，而视界熵则是真实的时空路径积分。2)目的是进一步理解之前发现的代数量化中的算子和状态，包括它们对熵和哈密顿量（时间演化）的影响。解决这个问题的一种方法是确定它与另一种协变相空间方法的关系，以及与所谓的角对称代数的关系，其他人已经在角对称代数上做了很多工作。此外，我们可以将处理扩展到允许空间域中的锥形奇点，手柄或黑洞。在第3章中，我们将尝试进一步了解引力异常与霍金辐射之间的关系，以及它与出射黑洞模式起源之谜之间的联系。此外，将尝试使用微扰量子引力来描述点之间预期的相关性猝灭，其中一个点在视界附近。4)项下的项目将设计和解释量子化声子场的模拟量子场理论测量，与马里兰玻色-爱因斯坦凝聚体小组合作。5)项下的项目将制定理想等离子体中固定磁螺旋度下能量最小化的广义相对论理论，以及黑洞和中子星等具有允许螺旋注入边界的区域的相对螺旋度理论。6)项下的项目将使用非固定视界发生器探测黑洞视界的本质，以更好地了解视界的结构及其曲率奇点在无限过去或未来的可能性。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。

The grant will support research projects on several aspects of gravitational physics where curved spacetime plays a key role. One group of topics pertains to the outstanding fundamental problem of understanding the quantum nature of spacetime. Specifically, research will be carried out pursuant to the nature of quantum states of spacetime. Much of this work focuses on the peculiar role of event horizons, since that is thought to be a promising window on the mysteries of quantum gravity. Other work will be directed at probing the validity of Einstein's theory of gravity by exploring the theoretical and observational consequences of certain modifications of that theory, particularly as that affects the behavior of black holes. A different component of the research will address questions about the behavior of magnetized plasma around astrophysical bodies like neutron stars and black holes, taking into account the effects of curved spacetime. This work could contribute to a better understanding of observations of these objects and their surroundings made with radio telescopes. Finally, in collaboration with an experimental atomic quantum fluid research group, research will be directed at exploring and exploiting the analogy between physics of quantum fluids and fields in curved spacetime, such as in the expanding universe. The results of the proposed research will be disseminated through written articles, as well as seminars, conference talks, and colloquia, and will contribute to our understanding of fundamental questions, as well as to observations and experiments in a more interdisciplinary fashion. The PI will provide instruction and mentoring to graduate and undergraduate students, regarding scientific research, writing, and verbal communication. The PI will design and implement instruction in a University of Maryland summer programs for rising 9th graders and for high school girls interested in physics. All of these activities will contribute to technical training and scientific literacy, as well as understanding and appreciation of the insights of physics.The main areas of work concern: 1) path integral methods for computing horizon entropy in quantum gravity ensembles, 2) non-perturbative reducedphase space quantization of a compact domain in 2+1-dimensional gravity, 3) the origin of outgoing black hole modes, 4) analog quantum field theory in a Bose-Einstein condensate, 5) general relativistic treatment of magnetic helicity around black holes and neutron stars, and 6) black hole horizons in Lorentz-violating gravity theories. Under 1), one project will study the relation between the nonperturbative path integral approach and the recent semiclassical analysis using algebraic quantum field theory, and another will interrogate the role of the near-horizon imaginary time evolution method in computing horizon entropy with an otherwise real spacetime path integral. Under 2) the aim is to further understand the operators and states in the algebraic quantization found previously, including their implications for entropy and Hamiltonian (time evolution). One approach to this will be to determine the relation to the alternative, covariant phase space approach, and to the so-called corner symmetry algebra, on which much work has been done by others. Further, we may extend the treatment to allow for conical singularities, handles, or a black hole in the spatial domain. Under 3) an attempt will be made to improve understanding of the relation between gravitational anomalies and Hawking radiation, and its connection to the puzzle of the origin of the outgoing black hole modes. Additionally, an attempt will be made to use perturbative quantum gravity to characterize the expected quenching of correlations between points, one of which is near a horizon. Projects under 4) will design and interpret analog quantum field theory measurements of the quantized phonon field, working together with the Maryland Bose-Einstein condensate group. Projects under 5) will formulate the general relativistic theory of energy minimization at fixed magnetic helicity in ideal plasmas, as well as of relative helicity in domains like black holes and neutron stars with boundaries allowing for helicity injection. Projects under 6) will probe the nature of black hole horizons with non-stationary horizon generators, to better understand how the horizon structure and the possibility of its curvature singularities in the infinite past or future.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.