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

我计划推进我们对我们宇宙最令人费解的特征之一：黑洞的理解。我的研究项目的范围从天体物理到数学物理。我的最终目标是从所有可能的方向完全理解黑洞，把广泛分离的黑洞物理学领域聚集在一起，寻找新的联系，并进行观测/实验验证。在接下来的五年里，我将专注于四个基本感兴趣的话题。*1)隐藏对称性。*我将利用我在辨别黑洞动力学(隐藏)对称性结构方面的专业知识，发展一种将波动方程与弯曲时空中的自旋相结合的数学理论。所得结果将应用于混凝土黑洞，研究它们的稳定性、准简正模和霍金辐射。一般理论将推动数学技术的进步，并为构造爱因斯坦方程的解提供新的工具。我的愿景是为超越引力物理的隐藏对称性的应用开辟新的视野。*2)黑洞热力学。*我在黑洞热力学方面的最新发现表明，黑洞的行为类似于化学体系，具有热、三点和重入相变。我将利用这些知识来获得新的发现，从发现新的黑洞相变到规范-重力二元性的应用/新课程。*3)类比引力。*我将研究类比引力模型，其中潜在的非引力现象模仿黑洞和有引力的系统的特征行为。这将为引力理论的本质带来新的见解，其中一些可能会在实验室实验中观察到。它很可能会影响更远的科学学科--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)天体物理黑洞。*最后，我计划研究更复杂、更现实的黑洞的性质，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，并可能为更深入地了解我们宇宙中的黑洞提供线索。*在我的项目中工作的研究生将接受多学科培训，学习高等数学和数学建模，发展分析创造性思维。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的理解。所有这些发展都将加强加拿大在理论物理和高素质人才培训方面的领先地位。

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.**