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

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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.**