推广准拓扑引力若干问题的研究

General relativity suffers from the ultraviolet divergence in both classical and quantum levels. The addition of higher derivative terms can yield a renormalizable theory, but leads to the appearance of massive spin 2 ghost. This ghost will break down the unitary of quantum theory and results to an unstable vacuum. Generalized quasi-topological gravity (GQG) is a class of higher derivative gravities with good properties, such as the absence of linear ghost in maximally symmetric backgrounds, the equation of motion is still second order in the context of spherically symmetric metrics and depends on only a single metric function. This project will study the classical properties of GQG, including black hole thermodynamics, phase transitions of black holes, classical verification of gravity theories. We will also study the application of GQG in gauge/gravity duality and the gravity/fluid duality. Then we study the application of GQG in cosmology. The research of this project will provide us with new insights into general relativity, and is very significant for studying the classical and quantum corrections.

广义相对论无论在经典还是量子层面都存在紫外发散问题。引入高阶曲率相互作用，可以使得引力能重整化，但会带来有质量的自旋为2的鬼场。这些鬼场会破坏量子理论的幺正性，使得真空变得不稳定。推广准拓扑引力是一类性质优良的高阶导数引力理论，在最大对称背景下没有线性鬼场，在球对称度规拟设下运动方程没有高阶导数，而且只由一个度规函数刻画。本项目将研究推广准拓扑引力的经典性质，包括黑洞热力学、黑洞相变、引力理论的经典验证。我们还将研究推广准拓扑引力在规范引力对偶中的应用以及推广准拓扑引力的流体对偶。最后我们还要研究推广准拓扑引力在宇宙学上的应用。通过本项目的研究可以为我们提供关于广义相对论新的认识，对于研究广义相对论的经典以及量子修正具有重要的理论意义。

本项目研究推广准拓扑引力在黑洞物理和引力波方面的应用。我们详细讨论了转动黑洞阴影形状的描述，给出了光子球和阴影半径的广义定义，从而将关于视界、光子球、阴影半径和黑洞质量的系列不等式推广到了一般稳态时空。我们分析了量子效应对于黑洞阴影和光环的影响，给出了一个利用光环来区分极端致密天体和黑洞的观测手段。我们研究了推广准拓扑引力的Blandford-Znajek过程，计算了提取能量的效率。我们将继续研究推广准拓扑引力的黑洞扰动、准正则模式和引力波铃宕。在项目执行期间，我们发表了三篇有影响力的高水平学术论文。