标题： 广义相对论笔记 显示英文标题

标题： Advanced General Relativity Notes

摘要： 这些讲义旨在为已经熟悉基本广义相对论的研究生读者提供指导。 它们以简洁的方式介绍了在研究引力时遇到的一些高级概念和问题。 这些笔记涵盖了：施瓦茨希尔德解的替代形式，包括经典的克鲁斯卡尔扩展；共形、卡特-彭罗斯图的构建说明；对比尔霍夫定理的讨论；对测地线和流形工具的讨论，包括能量条件；对视界和一些奇点定理的探讨；对克尔黑洞解性质的探索，包括佩诺斯过程和黑洞热力学；对埃克特和以色列-斯图尔特相对论热力学的讨论；对相对论中四维标架、爱因斯坦-嘉当理论和纽曼-彭罗斯形式主义的讨论；从哈密顿-雅可比形式主义出发的测地线方法计算的明确说明；从最小作用量原理推导相对论中陀螺运动的运动方程，即M.P.D.方程。 显示英文摘要

摘要： These lecture notes are intended as a guide to Graduate level readers that are already familiar with basic General Relativity. They present in a concise way some advanced concepts and problems encountered in the study of gravitation. In these notes are covered: Alternates forms of the Schwarzschild Black Hole solution, including the classic Kruskal extension; An account of the building of Conformal, Carter-Penrose, diagrams; A discussion of Birkhoff Theorem; A discussion of tools for Geodesics and congruences, including Energy Conditions; A discussion of Horizons and an approach to some of the singularity theorems; An exploration of the Kerr Black Hole solution properties, including the Penrose Process and Black Hole Thermodynamics; A discussion of the Eckart and Israel-Stewart Relativistic Thermodynamics; A discussion of Tetrads in Relativity, in Einstein-Cartan theory and in Newman-Penrose formalism; An explicitation of calculations on Geodesics approach from Hamilton-Jacobi Formalism; A derivation from Least action of the equation of Motion of a top in Relativity, the M.P.D. equations