Theoretical Aspects of Black Hole Physics

我计划增进我们对我们宇宙中最迷人的特征之一：黑洞的理解。我的研究计划侧重于这些物体的理论方面。我的长期目标是开发研究黑洞扰动的新技术，了解黑洞热力学的含义，并将黑洞的基本性质与观测联系起来。在接下来的5年里，我将专注于四个根本感兴趣的话题。 1)黑洞热力学 我最近在黑洞热力学方面的发现标志着如今一门名为黑洞化学的新学科的开始。我将利用我的专业知识在这个背景下研究黑洞。其目的是对黑洞的量子统计性质提供进一步的见解，找到更完整的热力学词典，并对规范/引力二元性提出新的挑战。 2)黑洞微扰 所有维度的旋转黑洞时空都承认了一种显着的隐藏对称性，这使得人们能够研究其附近各种物理场的行为。作为弯曲空间中隐藏对称性和场方程主题的领先专家，我的目标是解决剩余的长期难题：如何利用这种隐藏的对称性来研究引力扰动？这将为研究这些黑洞的稳定性、准正交模和霍金辐射开辟新的天地。同时，它将推动数学技术的进步，并为构建爱因斯坦方程的新解提供工具。 3)引力波 随着LIGO的开创性发现，引力波成为当今引力研究的前沿。我计划测试一种新的四极公式，用于计算由二元黑洞合并产生的引力波信号，该公式考虑了我们宇宙的宇宙膨胀的影响。 4)量子方面 量子效应在弯曲空间中尤其有趣，因为它们改变了粒子和局域性的基本概念。我将研究多视界时空中的粒子产生，探索惯性标架拖曳的非局域探测的可能性，并调查等价原理的违反。 在我的研究组工作的学生将受益于滑铁卢大学周边研究所世界一流的培训环境。他们将参与前沿研究，学习高等数学和数学建模。他们对任何需要独立、分析和创造性思维的领导职位的需求都很高。 我们的工作将影响各个学科(从纯数学到天体物理)，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基础研究、理论物理和高素质人才培养方面的领先地位。

I plan to advance our understanding of one of the most fascinating features of our Universe: black holes. My research program focuses on theoretical aspects of these objects. My long-term goals are to develop new techniques for studying black hole perturbations, to understand the implications of black hole thermodynamics, and to connect the fundamental properties of black holes with observations. In the next 5 years, I will concentrate on four topics of fundamental interest. 1) Black hole thermodynamics My recent discoveries in black hole thermodynamics marked the beginning of a new discipline nowadays called the black hole chemistry. I will use my expertise to study black holes in this context. The aim is to provide further insights into the quantum statistical nature of black holes, find a more complete thermodynamic dictionary, and raise new challenges for the gauge/gravity duality. 2) Black hole perturbations Rotating black hole spacetimes in all dimensions admit a remarkable hidden symmetry that allows one to study the behavior of various physical fields in their vicinity. As a leading expert on the subject of hidden symmetries and field equations in curved space, I aim to resolve the remaining long-standing puzzle: how to exploit this hidden symmetry for the study of gravitational perturbations? This will open new horizons for studying the (in)stability of these black holes, their quasinormal modes, and Hawking radiation. At the same time it will advance mathematical techniques and provide tools for constructing new solutions of Einstein's equations. 3) Gravitational waves With the ground-breaking discovery by LIGO, gravitational waves are at the forefront of gravitational research today. I plan to test a novel quadrupole formula for calculating the gravitational wave signatures produced by a binary black hole merger that take into account the effect of the cosmological expansion of our Universe. 4) Quantum aspects Quantum effects are especially interesting in curved space where they modify the fundamental notions of particles and locality. I am going to study the particle production in spacetimes with multiple horizons, probe a possibility of non-local detection of inertial frame dragging, and investigate the equivalence principle violations. The students working in my research group will benefit from the world-class training environment of the Perimeter Institute/University of Waterloo. They will participate in cutting-edge research, learn advanced mathematics and mathematical modeling. They will be in high demand for any leading positions that require independent, analytic, and creative thinking. Our work will impact various disciplines (ranging from pure mathematics to astrophysics) and may revolutionize our understanding of gravitational and black hole physics. All these developments will reinforce the leading role of Canada in basic research, theoretical physics, and training of highly qualified personnel.