General Relativity: An Informal Primer

General relativity, and its application to cosmological models such as inflation, is a remarkably beautiful and elegant theory. Yet newcomers to the field often face at least three types of challenges: conceptual, mathematical, and notational. Over the past century, physicists and mathematicians have developed a remarkably compact formalism and notation for working with general relativity, which requires some practice to really get comfortable with. The methods are quite powerful and well worth the investment of effort. One can only really hope to tackle the fascinating conceptual and mathematical challenges if one has first gotten over the hurdle of understanding how to parse and manipulate the formalism. These notes are intended to give an informal and very brief introduction to working with general relativity. They are certainly no substitute for a real textbook; rather, they are geared to be read in conjunction with a book like Steven Weinberg’s Gravitation and Cosmology [1], to provide a little extra practice unpacking the unfamiliar notation so that students may dig in to the real meat of Weinberg’s book. Think of these notes, in other words, like “language lab”: before one can engage at a deep level with the novels of Molière or the philosophy of Hegel, one must gain at least a rudimentary familiarity with the medium of composition. Weinberg’s textbook is aimed at graduate students. Some more accessible books, aimed at advanced undergraduates, have appeared in recent years, and these might be helpful as additional references, including Wolfgang Rindler’s Relativity: Special, General, and Cosmological [2] and Tai-Pei Cheng’s Relativity, Gravitation, and Cosmology: A Basic Introduction [3]. Cheng’s notation is closer to Weinberg’s, and hence to the notation we will be using. Rindler introduces his own notation that has some advantages on its own terms but which does not exactly match that of Weinberg or the others.