Theoretical Aspects of Black Hole Physics

我计划推进我们对宇宙中最迷人的特征之一的理解：黑洞。我的研究计划侧重于这些对象的理论方面。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，并将黑洞的基本特性与观测联系起来。未来5年，我将重点关注四个根本性的问题。我最近在黑洞热力学方面的发现标志着一门新学科的开始，这门学科现在被称为黑洞化学。我将利用我的专业知识在这种背景下研究黑洞。其目的是为黑洞的量子统计性质提供进一步的见解，找到一个更完整的热力学字典，并为规范/重力对偶提出新的挑战。2)黑洞微扰在所有维度上旋转的黑洞时空具有一种显著的隐藏对称性，使人们能够研究其附近各种物理场的行为。作为研究弯曲空间中隐藏对称性和场方程的顶尖专家，我的目标是解决一个长期存在的难题：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、它们的准正态模式和霍金辐射开辟新的视野。同时，它将推进数学技术，并为构造爱因斯坦方程的新解提供工具。随着LIGO的突破性发现，引力波成为当今引力波研究的前沿。我计划测试一个新的四极公式，用于计算双黑洞合并产生的引力波特征，该公式考虑了我们宇宙的宇宙膨胀效应。4)量子方面量子效应在弯曲空间中特别有趣，因为它们改变了粒子和局域性的基本概念。我将研究多重视界时空中的粒子产生，探索非局部检测惯性系拖拽的可能性，并研究等效原理的违反。在我的研究小组工作的学生将受益于圆周研究所/滑铁卢大学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都有很高的需求。我们的工作将影响各个学科（从纯数学到天体物理学），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基础研究、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 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.