标题： 一个简洁精炼的现代广义相对论入门 显示英文标题

标题： A Lean and Mean Introduction to Modern General Relativity

摘要： 为奥克兰大学物理系748课程“广义相对论导论”准备的笔记。它们旨在直接使用微分几何的现代语言，但以物理动机的方式向高年级本科生介绍广义相对论，并在整个过程中保持从一节到另一节、从一章到另一章的逻辑连贯性。因此，它们不可避免地涵盖了若干在入门课程中通常不涉及或从新视角探讨的主题。这些主题包括但不限于：仿射空间，将二阶张量与矩阵进行比较和对比，流形上的积分，Rindler度规，包括施瓦茨希尔德度规的正确近源边界条件，从Rindler视角出发研究Kruskal-Szekeres坐标等。 显示英文摘要

摘要： Notes prepared for the introductory general relativity course PHYSICS 748 at The University of Auckland. They are designed to introduce general relativity to upper-year undergraduate students directly using the modern language of differential geometry but in a physically motivated way, and throughout keeping a logical flow from section to section and chapter to chapter. In doing so, they necessarily cover a number of topics either not normally treated in an introductory course, or from a novel perspective. These include for example: affine spaces, comparing and contrasting rank-2 tensors with matrices, integration on manifolds, the Rindler metric, including a proper near-source boundary condition for the Schwarzschild metric, approaching Kruskal-Szekeres coordinates from a Rindler perspective, and more.