An Introduction to General Relativity and Cosmology

Experts Plebański and Krasiński provide a thorough introduction to the tools of general relativity and relativistic cosmology. Assuming familiarity with advanced calculus, classical mechanics, electrodynamics and special relativity, the text begins with a short course on differential geometry, taking a unique top-down approach. Starting with general manifolds on which only tensors are defined, the covariant derivative and affine connection are introduced before moving on to geodesics and curvature. Only then is the metric tensor and the (pseudo)-Riemannian geometry introduced, specialising the general results to this case. The main text describes relativity as a physical theory, with applications to astrophysics and cosmology. It takes the reader beyond traditional courses on relativity through in-depth descriptions of inhomogeneous cosmological models and the Kerr metric. Emphasis is given to complete and clear derivations of the results, enabling readers to access research articles published in relativity journals.

專家Plebański和Krasiński提供了對廣義相對論和相對論宇宙學工具的全面介紹。假設讀者對高等微積分、古典力學、電動力學和特殊相對論有所了解，本書以一個獨特的自上而下的方式開始，提供了一個關於微分幾何的簡短課程。從僅定義了張量的一般流形開始，引入了協變導數和仿射連接，然後轉向測地線和曲率。然後才引入度量張量和（偽）黎曼幾何，將一般結果特化到這種情況。主要內容描述了相對論作為一種物理理論，並應用於天體物理學和宇宙學。通過對非均勻宇宙模型和Kerr度量的深入描述，本書使讀者超越傳統的相對論課程。強調對結果的完整和清晰的推導，使讀者能夠閱讀相對論期刊上發表的研究文章。