引力场方程的精确解及其宇宙学应用

Exact solutions of gravity field equation is a classical and important subject. Many exact solutions have been found since the birth of Einstein field equation. However,the physical meanings of most solutions are not clear. It is really no better way to pin down the physical meaning of a solution than to find the matter source which generates the solution in question. Several important exact solutions will be studied in this project, especially the sources of plane symmetric and cylindrical symmetric solutions. These solutions are very difficult, even were regarded to be impossible before our solution for the source of Taub solution. In this project, we shall take full consideration of the key role of the matter with negative pressure in the new solution, which is inspired by the recent breakthrough in cosmology. Based on this idea, we have obtained a new class of plane symmetric solution in a series of studies, proving that a special family in this solution is the proper source of the vacuum plane symmetric solution (Taub solution). Taub solution has been "proved" to be impossible to match to any matter source. In this project we shall study the applications in cosmology and holographic properties of this new class of plane symmetric solution. We shall also explore the source for cylindrical symmetric solution, exact solutions in modified gravity theories， for example the sclar-tensor theory and the related problems in cosmology，especially the dark energy problem in cosmology.

引力场方程的精确解是一个经典而重要的领域。自爱因斯坦方程诞生至今，大量的精确解已经得到。但毋庸讳言，绝大多数解的物理意义尚不清楚。要明确一个真空解的物理意义，最好的方法莫过于找到产生这个真空解的物质场。本课题将研究理论上非常重要的几类精确解，尤其是具有平面对称性和柱对称性的精确解的源。这样的解传统上极为困难，在申请人成功找到Taub解的源之前甚至被认为不可能。在本课题中，申请人将充分吸收来自宇宙学研究的最新成果，即考虑具有负压强的特殊物质在新解中的关键作用。沿该思路，申请人在一系列工作中得到一类新的平面对称解，并证明其中一个特别的参数族正是真空平面对称解（Taub解）的源，而此前Taub解已被数个工作"证明"是不可能存在物质源的。本课题将继续研究该解的宇宙学应用，全息性质等。同时探索柱对称解的源以及其他引力理论,例如标量-张量理论的精确解和与之紧密相关的宇宙学问题，尤其是暗能量问题。

引力场方程的精确解是一个经典而重要的课题。本项目开创了热力学方法直接得到场方程精确解的方案。在该方案中，引力场方程的能量及其所处系统的热力学性质是非常关键的。引力场的能量（质量）是一个困难的课题。一方面引力场必然带有能量，否则引力波将失去意义。另一方面，等效原理使得协变的能动张量密度的定义变得不可能。在这种约束下，最好的结果是定义准局域能量。准局域能量有多种不同的形式，负责人发现，Misner-Sharp能量是系统的绝热能量，并用此结论导出了多个精确解，包括史瓦西解、史瓦西-德西特解、Reissner-Nordstrom 解等。进一步的，负责人将其推广到了修改引力论框架下，首次得到了f（R）的精确解，该解此前未用其他方法得到。同时，本项目还研究了三维f（R）引力的精确解和引力波，有质量引力的热力学，退化度规下有质量引力的无鬼性，黑洞超辐射的稳定性等问题。