Relativistic Astrophysics and Gravitation Physics

这个项目的主要目的是在各种可能的时空流形和各种物理上有趣的物质源上发展一种严格的非均匀宇宙学方法，并研究这一理论的潜在应用。作为第一步，Vincent Moncrief计划完成他对长期存在的非均匀、非对称、真空时空大家族的研究，这些时空从过去的大爆炸奇点爆炸，在未来膨胀到无限的体积。这些时空，虽然代表了已知参考解的某些足够小的（尽管是完全非线性的）扰动，但在膨胀的早期阶段可以具有任意大的时空曲率。下一步将在分析中包括各种有趣的物质源，并尝试将长时间存在的结果扩展到包含非真空解决方案，例如电磁场和杨-米尔斯场，完美流体和弗拉索夫流体，也许还有稳定因果类型的不完美流体。这项研究将阐明现代万有引力理论和宇宙学的基础

***9732629MoncriefThe main aim of this project is to develop a rigorous approach to inhomogeneous cosmology on a wide variety of possible spacetime manifolds and with a variety of physically interesting matter sources and to investigate potential applications of this theory. As a first step Vincent Moncrief plans to complete his investigations of the long-time existence of large families of inhomogeneous, non-symmetric, vacuum spacetimes which explode from a big bang singularity in the past and expand to infinite volume in the future. These spacetimes, though representing certain sufficiently small (though fully non-linear) perturbations of known reference solutions, can have arbitrarily large spacetime curvatures in the early stages of expansion. The next step will be to include a variety of interesting matter sources in the analysis and attempt to extend the long-time-existence results to non-vacuum solutions containing, e.g., electromagnetic and Yang-Mills fields, perfect and Vlasov fluids and perhaps imperfect fluids of stable-causal type.This research will clarify the foundations of modern gravitation theory and cosmology.***