Bianca Dittrich, Philipp A. Hoehn, Tim A. Koslowski, Mike I. Nelson
备注：
6 pages + references -- matches published version (clarifications added for why GR with cosmologically interesting matter likely fails our notion of weak-integrability)
Full general relativity is almost certainly 'chaotic'. We argue that this entails a notion of nonintegrability: a generic general relativistic model, at least when coupled to cosmologically interesting matter, likely possesses neither differentiable Dirac observables nor a reduced phase space. It follows that the standard notion of observable has to be extended to include non-differentiable or even discontinuous generalized observables. These cannot carry Poisson-algebraic structures and do not admit a standard quantization; one thus faces a quantum representation problem of gravitational observables. This has deep consequences for a quantum theory of gravity, which we investigate in a simple model for a system with Hamiltonian constraint that fails to be completely integrable. We show that basing the quantization on standard topology precludes a semiclassical limit and can even prohibit any solutions to the quantum constraints. Our proposed solution to this problem is to refine topology such that a complete set of Dirac observables becomes continuous. In the toy model, it turns out that a refinement to a polymer-type topology, as e.g. used in loop gravity, is sufficient. Basing quantization of the toy model on this finer topology, we find a complete set of quantum Dirac observables and a suitable semiclassical limit. This strategy is applicable to realistic candidate theories of quantum gravity and thereby suggests a solution to a long-standing problem which implies ramifications for the very concept of quantization. Our work reveals a qualitatively novel facet of chaos in physics and opens up a new avenue of research on chaos in gravity which hints at deep insights into the structure of quantum gravity.
Leinweber Institute for Theoretical Physics and Department of Physics, University of California, Berkeley（加州大学伯克利分校莱因韦伯理论物理研究所和物理系）；Leinweber Institute for Theoretical Physics, Stanford University（斯坦福大学莱因韦伯理论物理研究所）；Physics Department, University of Washington（华盛顿大学物理系）
Probing Quantum Gravity through Chaotic Orbits and Strong-Field Effects in Kerr Black Holes Embedded in Perfect Fluid Dark Matter
The Institute of Mathematical Sciences, C.I.T. Campus（泰米鲁纳德邦金奈塔拉马尼 CIT 校区的数学科学研究所）；Khazar University（阿塞拜疆巴库的哈萨尔大学）；University of Mazandaran（伊朗巴巴萨尔的马赞达兰大学）；Virtual University of Pakistan（巴基斯坦拉合尔的虚拟大学）；Hemwati Nandan Bahuguna Garhwal University（印度北阿坎德邦斯里纳加的赫姆瓦蒂·南丹·巴胡加纳加尔瓦尔大学）；Harbin Institute of Technology（中国哈尔滨的哈尔滨工业大学）；Zhejiang Normal University（中国金华的浙江师范大学）
Horizon--orbit scale competition underlying chaos bound violation for spinning particles
School of Science, Xihua University（西华大学理学院）；Center for Gravitational Wave Experiment, National Microgravity Laboratory, Institute of Mechanics, Chinese Academy of Sciences（中国科学院力学研究所微重力实验室引力波实验中心）
最近的研究表明，除了超时有序关联函数（OTOC）外，量子混沌在能量密度两点函数中也有明显的表现，至少在极大混沌系统中是如此.的表现，称为极点跳跃，涉及的分析行为的能量密度两点函数周围的一个特殊的点$ω= i λ$，$k = i λ/v_B$在复杂的频率和动量平面。这里$λ$和$v_B$是表征量子混沌的李雅普诺夫指数和蝴蝶速度。本文论证了跳极现象对于一般的有限温度系统是普遍存在的。在这样做的过程中，我们发现了一个令人惊讶的通用功能的线性爱因斯坦方程周围的静态黑洞几何。我们还研究了分析全息轴子模型，我们的一般论点的所有功能，以及极点跳跃现象可以详细验证。
