基本含时黑洞解及其性质研究

Time-dependent black hole solutions (describing the formation of black holes) are expected to offer a distinctive perspective on important problems in gravity, but there is relatively little study about them. The reason is that, it is very difficult to obtain explicit time-dependent black hole solutions. Most early examples are constructed by deriving their stress energy tensor from the Einstein equations (there is improvement to this situation only recently). Besides, we still do not have a systematic method in studying their properties. For such reasons, we want to use various methods (symmetry assumption, scalar potential reconstitution, warped embeddings, etc) to construct more time-dependent black hole solutions with explicit fundamental matter source (we shall call them fundamental time-dependent black hole solutions). Then we want to develop a systematic method to study their physical properties and to discuss related fundamental problems. In more detail, we want to do the following: (1) Consider Einstein gravity coupled to a fundamental matter field (e.g. a scalar field) and construct time-dependent black hole solutions; (2) Study the causal structure of these solutions, discuss their physical properties, such as the initial and final states of the evolving space-time and energy transportation, and try to develop a theory of black hole formation for general matter source; (3) Study the thermodynamics, phase transition, and quantum properties of these solutions. The purpose of this project is to focus on the fundamental time-dependent black hole solutions and their physical properties. We expect such study to shed light on important problems such as black hole formation, development of space-time singularities, cosmic censorship and gauge gravity duality in dynamical space-times.

描述黑洞形成的含时黑洞解可以为引力理论中的一些关键问题提供独特的视角，但对其研究一直都非常欠缺。原因是含时黑洞解很难构造，以前获知的含时黑洞解其能动量张量都是由引力场方程反推来得到（这种情况直到最近才有所改善），而且人们也缺乏研究其性质的有效方法。项目拟通过对称性假设，标量势重构和翘曲分解等方法，针对一些基本物质场构建新的含时黑洞解（我们称之为基本含时黑洞解以示区别），并研究其性质。具体研究内容包括：（1）考虑爱因斯坦引力耦合基本物质场，如标量场，构造新的含时黑洞解；（2）系统研究含时黑洞解的全局和局部时空结构，讨论其性质，包括时空初末态和随时间演化中的能量输运等问题，建立一般物质形成黑洞的理论框架；（3）研究含时黑洞解的热力学性质，相变性质和量子性质等问题。项目旨在通过研究含时黑洞解及其性质，为研究黑洞形成，时空奇点的产生或规避，动态过程中的规范引力对偶等基本和重要物理问题提供具体实例。

构建描述黑洞形成的含时黑洞解是引力理论的重要研究课题，但是由于研究困难，对此研究比较稀缺。本项目主要目标为爱因斯坦-标量引力理论中的基本含时解，很好地构建了三维爱因斯坦-标量引力理论中的不带电含时解、带电静态解和含时解、非线性带电静态解、加速解和对应的含时解。分析了对应含时时空的表观视界和全局结构，并检验了宇宙监督假设，发现了其成立对标量场塌缩形式的依赖。此外，本项目讨论了黑洞解在热力学方向的应用，包括quintessence暗能量影响下的RN-AdS黑洞的精确相结构、Horava引力中AdS黑洞具有的lambda相变和含标量时空等修改引力时空中的熵关系和熵界等。这些研究，对讨论静态时空和含时时空的性质有着重要的作用，也为讨论引力性质、全息性质和热力学性质等提供了很好的背景；为研究双星系统并合时时空性质和结构的讨论提供了线索，从而可以沿此切入双星并合时含时时空性质的研究，为引力波的研究提供帮助；也为讨论引力的量子性质提供了一些有趣的观点和前进方向。