Facing black hole crises Black hole thermodynamics, the information paradox, and non-local effects

This doctoral thesis studies issues related to black hole physics and other aspects of gravity theory, including black hole thermodynamics, the information paradox, asymptotic symmetries, and emergent gravity. After reviewing some relevant concepts and basic ideas of black hole physics, we use the Euclidean path integral to evaluate the partition functions of gauge theory on different black hole backgrounds. Special attention should be paid to the super-low temperature limit, where we have extra entropy contributions from zero modes and boundary stretched Wilson lines. Then, we focus on the role of soft hair in understanding the black hole information paradox. Soft hair can be regarded as an important ingredient in reconstructing interior operators; we derive an effective action for the soft hair modes and get one version of the Page curve by comparing the rates of Hawking radiation and soft hair measurement. The last part is devoted to emergent gravity, where we use the Casini-Bekenstein bound and the entanglement first law to reproduce some concepts in gravity theory. Besides the aforementioned topics, the thesis also discusses other related topics like black hole phase transition, the island prescription, and wormholes.