Quantum theory, black holes and quantum gravity

最近的引力波探测表明，一个新的宇宙观测窗口的前景正在实现。其中第一次观测，即2016年探测到10亿年前两个黑洞合并发出的引力波，令人震惊地证实了爱因斯坦引力理论在强场区域的有效性，并首次直接证明了黑洞的存在。根据爱因斯坦的理论，在每个黑洞的中心都有一个奇点，一个高密度和高曲率的区域，已知的物理定律在这里被打破。1976年，霍金证明了量子过程允许能量以热辐射的形式从黑洞中泄漏出来。这会导致黑洞缩小并有可能消失，而不会透露形成黑洞的物质的任何初始状态，从而不可逆转地破坏信息。奇点的存在和信息丢失的可能性是只有当量子力学和引力成功地统一到一个做出可证伪预测的完整理论中时才能解决的问题。在没有这样的理论的情况下，人们必须从模型中获得洞察力，这些模型旨在包含尽可能多的完整理论的基本特征，同时在数学上是易于处理的。我的研究将集中在这样的模型背景下黑洞的量子行为。我的长期目标是找到通用属性，这些属性将允许对强场黑洞动力学和蒸发进行稳健的、最终可观察到的量子修正预测。具体主题包括：在一类新的有效球形模型内非奇异黑洞形成和蒸发的动力学；各种球形黑洞的量子力学，包括奇点分辨率的能谱和动力学；形成能壳(“防火墙”)的量子场论模型，该模型旨在防止信息消失在事件视界以下，从而部分解决黑洞信息损失问题；在超导体和夸克-胶子等离子体等各种物理系统的全息描述背景下，研究流动方程，这是广义热方程的一种形式。 对加拿大的好处：这项工作将为学生提供物理培训、研究经验和解决问题的技能，这将极大地扩大他们的职业选择。它还将推动我们走向物理学中下一个范式转换的突破：一个一致的、可验证的引力量子理论。无法预测这种突破何时会发生，但当它们发生时，它们会改变我们对世界的看法，并带来不可预见和无价的技术进步。

Recent gravitational wave detections suggest that the promise of a new observational window on the universe is being realized. The first of these observations, namely the 2016 detection of gravitational waves emitted a billion years ago by the merger of two black holes, provided astounding confirmation of the validity of Einstein's theory of gravity in the strong field region as well as the first direct evidence for the existence of black holes. According to Einstein's theory, at the center of every black hole there exists a singularity, a region of high density and curvature where the known laws of physics break down. In 1976 Hawking showed that quantum processes allow energy to leak out of black holes in the form of thermal radiation. This causes the black hole to shrink and potentially disappear without revealing anything about the initial state of the matter that formed the black hole, thereby irreversibly destroying information. The presence of singularities and the possibility of information loss are issues that can only be resolved once quantum mechanics and gravity are successfully unified into a complete theory that makes falsifiable predictions. In the absence of such a theory, one must obtain insights from models designed to contain as many essential features of the full theory as possible while being tractable mathematically. My research will focus on the quantum behaviour of black holes in the context of such models. My long term goal is to find generic properties that would allow robust and ultimately observable predictions for quantum corrections to strong field black hole dynamics and evaporation. Specific topics include: the dynamics of nonsingular black hole formation and evaporation within a new class of effective spherical models; the quantum mechanics of a large variety of spherical black holes, including the energy spectrum and dynamics of singularity resolution; a quantum field theory model for the formation of shells of energy (``firewalls”) that are designed to partially solve the black hole information loss problem by preventing information from disappearing below the event horizon; a study of flow equations, a form of generalized heat equation, in the context of holographic descriptions of various physical systems such as superconductors and the quark-gluon plasma. Benefit to Canada: This work will provide students with physics training, research experience and problem solving skills that will greatly expand their career options. It will also move us towards the next paradigm-shifting breakthrough in physics: a consistent and verifiable quantum theory of gravity. It is impossible to predict when such breakthroughs will occur, but when they do, they change our view of the world and give rise to unforeseeable and invaluable technological advances.