Mathematical Questions Resulting from the Coupling of Gravity to Other Fields

本项目研究广义相对论中的三个问题：（i）克尔（旋转）黑洞背景度规中电磁和线性引力波解的稳定性;即，在黑洞视界外，给出了这些具有紧支撑初值的偏微分方程的Cauchy问题的解。 这些稳定性结果将增加克尔度规在详细天体物理模型中使用的可信度。 (ii)从旋转黑洞中提取能量的彭罗斯过程的严格证明。 (iii)将古斯的暴胀理论纳入首席研究员的宇宙学模型。brbr自从爱因斯坦在1915年提出广义相对论以来，黑洞就引起了物理学家和数学家的兴趣。 人们对这些问题进行了深入研究，但许多问题仍然没有答案。 这个项目探讨了三个重要问题。 它研究在电磁和引力扰动下黑洞的稳定性。 这种认识对于预测源自外层空间的引力辐射的性质具有重要意义。 稳定性问题将被认为是在平行的天文学家所作的观察，导致更好的理论理解的数值模拟的解决方案爱因斯坦方程。 该项目还旨在将从旋转黑洞中提取能量的问题置于坚实的理论基础之上。 从旋转黑洞中提取能量的想法早在1968年就提出了，但直到最近，这个问题仍然难以研究。 最后，该项目研究了天体物理学中涉及宇宙学和超新星爆炸的一些问题;这些经历引力坍缩的密度极高的大质量恒星的爆炸是宇宙中重元素的种子，包括碳和铁。

This project investigates three questions in general relativity: (i) The stability of solutions of electromagnetic and linearized gravitational waves in a Kerr (rotating) black hole background metric; i.e., solutions of the Cauchy problem for these partial differential equations with compactly supported initial data outside of the event horizon of the black hole. These stability results will add credibility to the use of the Kerr metric in detailed astrophysical models. (ii) Rigorous justification of the Penrose process for the extraction of energy from a rotating black hole. (iii) Incorporation of Guth's theory of inflation into the principal investigator's cosmological model. brbrBlack holes have interested both physicists and mathematicians since Einstein proposed his theory of general relativity in 1915. They have been studied intensively, but many questions remain unanswered. This project explores three important questions. It investigates the stability of black holes under electromagnetic and gravitational perturbations. Such understanding is of great importance for predicting the nature of gravitational radiation originating in outer space. The stability problem will be considered in a manner parallel to the observations made by astronomers, leading to a better theoretical understanding of numerical modeling of solutions of Einstein's equations. The project also aims to put the question of extracting energy from a rotating black hole on a firm theoretical basis. The extraction of energy from a rotating black hole was proposed in 1968, but until recently the question was far too difficult to be studied. Finally, the project studies some questions in astrophysics dealing with cosmology and supernova explosions; these explosions of enormously dense massive stars undergoing gravitational collapse are responsible for seeding the universe with heavy elements, including carbon and iron.