黑洞是广义相对论的重要预言和研究对象。 霍金用弯曲时空量子场论的方法证明了黑洞热辐射的存在，进而为黑洞热力学的建立奠定了基础。 黑洞热力学规律一直是研究的热点方向。 随着宇宙学观测及相关学科的发展， 爱因斯坦引力之外的引力理论，即修正引力理论越来越受到学术界关注， 黑洞热力学定律不仅在广义相对论框架内，而且在其它引力理论中被不断检验和挑战。 本项目拟研究的相关问题包括：通过对作用量变分推导带宇宙学常数以及高阶曲率引力理论的黑洞第一定律； 考察一般微分同胚不变引力理论下的黑洞第二定律；通过计算粒子的self-force 检验宇宙监督假设及热力学第三定律； 通过热力学的熵最大化原理推导爱因斯坦场方程以及其它引力理论中相应的场方程。

General relativity predicted the existence of black hole, which has been an important research subject. Hawking proved that black holes can radiate as thermal objects and then established the foundation of black hole thermodynamics. With the improvement of cosmological observations, much attention has been paid to gravity theories beyond Einstein. Laws of black hole thermodynamics are tested not only within the framework of general relativity, but also by other modified gravity theories. This project attempts to investigate the following issues: Deriving the first law of black hole thermodynamics by variation of actions with cosmological constant and of higher-curvature gravity theories; Testing the second law of black hole thermodynamics for general diffeomorphism-invariant theories; Testing the cosmic censorship conjecture and the third law of black hole thermodynamics by calculating the self-force of particles; Deriving field equations in Einstein's theory and other gravity theories from the maximal entropy principles.