Black hole physics: hidden symmetries, thermodynamic analogies, and analogue gravity systems

我计划推进我们对宇宙中最令人困惑的特征之一的理解：黑洞。我的研究范围从天体物理学到数学物理。我的最终目标是从所有可能的方向完全理解黑洞，将黑洞物理学广泛分离的领域整合在一起，寻求新的联系和观测/实验验证。未来5年，我将重点关注四个根本性的问题。***1)隐藏的对称性。***我将利用我在识别黑洞动力学（隐藏）对称结构方面的专业知识，发展一种数学理论，用于在弯曲时空中积分波方程和自旋。所得结果将应用于具体黑洞，研究其稳定性、准正模和霍金辐射。广义理论将促进数学技术的发展，并为构造爱因斯坦方程的解提供新的工具。我的愿景是为隐藏的对称性在引力物理学之外的应用开辟新的视野。***2)黑洞热力学。***我最近在黑洞热力学方面的发现表明，黑洞的行为就像化学系统一样，具有焓、三相点和可重新进入的相变。我将利用这些知识来获得新的发现，从寻找新的黑洞相变到应用于/新的规重对偶性课程。***3)模拟重力。***我将研究模拟引力模型，其中潜在的非引力现象模仿黑洞和引力系统的特征行为。这将为引力理论的本质带来新的见解，其中一些可能在实验室实验中观察到。它可能会影响更遥远的科学学科——凝聚态物理、光学和流体力学——这些学科可能会受益于几何方法解决经典问题的全部力量。***4)天体物理学黑洞。***最后，我计划研究更复杂和现实的黑洞的性质，例如那些有磁场或可能被宇宙弦穿透的黑洞。这项研究将与天体物理观测相关，并可能为我们更深入地了解宇宙中的黑洞提供线索。***在我的项目中工作的研究生将受到多学科的训练，学习高等数学和数学建模，培养分析创造性思维。他们将沉浸在前沿研究中——我们的工作将影响各种物理学科，并可能彻底改变我们对引力和黑洞物理学的理解。所有这些发展都将加强加拿大在理论物理和培养高素质人才方面的领导作用

I plan to advance our understanding of one of the most baffling features of our Universe: black holes. The scope of my research program ranges from astrophysics to mathematical physics. My ultimate goal is to completely understand black holes from all possible directions, to bring together widely separated fields of black hole physics, seek new connections and observational/experimental verifications. In the next 5 years, I will concentrate on four topics of fundamental interest.***1) Hidden Symmetries.***I will use my expertise in discerning the structure of dynamical (hidden) symmetry in black holes to develop a mathematical theory for integrating wave equations with spin in curved spacetime. The obtained results will be applied to concrete black holes to study their stability, quasi-normal modes, and Hawking radiation. The general theory will advance mathematical techniques and provide new tools for constructing solutions of Einstein equations. My vision is to open new horizons for the application of hidden symmetries beyond gravitational physics.***2) Black hole thermodynamics.***My recent discoveries in black hole thermodynamics showed that black holes behave like chemical systems, having enthalpy, triple points, and re-entrant phase transitions. I will exploit this knowledge to obtain new discoveries, ranging from finding novel black hole phase transitions to applications in/new lessons for gauge-gravity duality. ***3) Analogue Gravity.***I will investigate analogue gravity models where the underlying non-gravitational phenomena mimic the characteristic behavior of black holes and systems with gravity. This will bring new insights into the nature of gravitational theory, some of them potentially observable in laboratory experiments. It may well impact more distant scientific disciplines -- condensed matter physics, optics, and fluid mechanics -- that may benefit from the full power of the geometric approach to their classical problems.***4) Astrophysical Black Holes.***Finally, I plan to study the properties of more complicated and realistic black holes, for example those with magnetic fields or perhaps penetrated by cosmic strings. This research will be relevant to astrophysical observations and may provide clues to deeper understanding of black holes in our Universe. ***The graduate students working in my program will be trained multidisciplinary, learn advanced mathematics and mathematical modelling, develop analytic creative thinking. They will be immersed in leading edge research - our work will impact various physical disciplines and may revolutionize our understanding of gravitational and black hole physics. All these developments will reinforce the leading role of Canada in theoretical physics and training of highly qualified personnel.**