渐进AdS几何，标量荷及黑洞热力学

There have been conitnuing interests in constructing new black holes and studying their global structures and thermodynamical properties. The folklore is that black holes are unique, solely determined by the conserved quantities such as mass and electric charges, which completely specify the first law of black hole thermodynamics. Our recent works demonstrate that the folklore is not always valid. In this proposal, we shall systematically study asymptotic AdS black holes and solitons supported by massive spin-0,1,2 fields, i.e. scalars, Proca vectors and massive gravitons.We shall demonstrate with explicit examples that black hole uniqueness theorem can be overcome. Furthermore, we shall demosntrate that although the massive fields we consider do not have conserved charges, they can nevertheless modify the familiar old first law of thermodynamics. Our results demonstrate that the first law has a more fundamental origin and that its previous connection to conserved charges is accidental and a consequence of fine tuning. This implies that those previously-known charged black holes in gauged supergravities that satisfy the usual first law constitute only a tiny portion of all the allowed black holes. There exist a large number of new black holes in gauged supergravities that satisfy the new first law of black hole thermodynamics. The new solutions and the first law are charaterised by the AdS boundary conditions of the massive fields we considered.They provide new AdS background geometries in supergravities and hence a new venue of investigating the AdS/CFT correspondence.

黑洞解的构造及其热力学性质的研究已有相当长的历史，积累了像黑洞"唯一性定理"及黑洞热力学和守恒量关系的一些"常识"。本项目的研究将突破以往常识。在AdS/CFT和规范超引力框架下，我们将系统地研究自旋分别为0，1，2的有质量标量场，矢量场和引力子场对渐进AdS黑洞和孤立子的贡献。首先我们证明黑洞的唯一性定理可以突破。其次我们考虑的物质场虽然没有守恒量，但他们依然可以修正我们以前熟知的黑洞热力学第一定律，从而证明第一定律是一个更加广泛并基本的定律，它和守恒量并没有一一对应的特殊关系。这个结果意味着，我们熟悉的那些满足已知黑洞热力学第一定律的规范超引力AdS黑洞解只是理论所允许的全部黑洞解的冰山一角，是精细微调的产物，还有更多的渐进AdS黑洞或孤立子解。这些新的渐进AdS几何在AdS/CFT的应用，目前还是一片空白。因此本项开拓了一个研究黑洞热力学新现象及其在AdS/CFT应用的新平台。

黑洞解的构造及其热力学性质的研究已有相当长的历史，积累了像黑洞“唯一 性定理”及黑洞热力学和守恒量关系的一些“常识”。本项目的研究将突破以往常识。在 AdS/CFT 和规范超引力框架下，我们将系统地研究自旋分别为 0，1，2 的有质量标量场，矢 量场和引力子场对渐进AdS黑洞和孤立子的贡献。首先我们证明黑洞的唯一性定理可以突破。 其次我们考虑的物质场虽然没有守恒量，但他们依然可以修正我们以前熟知的黑洞热力学第 一定律，从而证明第一定律是一个更加广泛并基本的定律，它和守恒量并没有一一对应的特 殊关系。这个结果意味着，我们熟悉的那些满足已知黑洞热力学第一定律的规范超引力 AdS 黑洞解只是理论所允许的全部黑洞解的冰山一角，是精细微调的产物，还有更多的渐进 AdS 黑洞或孤立子解。这些新的渐进 AdS 几何在 AdS/CFT 的应用，目前还是一片空白。因此本项 开拓了一个研究黑洞热力学新现象及其在 AdS/CFT 应用的新平台。本课题研究顺利，无需进行大的调整或变更。成果包含高阶导数引力中新黑洞的构造，及提出准拓扑里奇引力概念。共发表40篇SCI论文，一篇发表在PRL，其余发表在JHEP，PRD, PLB及EPJC。