A Mathematical Introduction to General Relativity
暫譯: 廣義相對論的數學導論
Sasane, Amol
- 出版商: World Scientific Pub
- 出版日期: 2021-08-22
- 售價: $3,280
- 貴賓價: 9.5 折 $3,116
- 語言: 英文
- 頁數: 500
- 裝訂: Quality Paper - also called trade paper
- ISBN: 9811256721
- ISBN-13: 9789811256721
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商品描述
The book aims to give a mathematical presentation of the theory of general relativity (that is, spacetime-geometry-based gravitation theory) to advanced undergraduate mathematics students. Mathematicians will find spacetime physics presented in the definition-theorem-proof format familiar to them. The given precise mathematical definitions of physical notions help avoiding pitfalls, especially in the context of spacetime physics describing phenomena that are counter-intuitive to everyday experiences.In the first part, the differential geometry of smooth manifolds, which is needed to present the spacetime-based gravitation theory, is developed from scratch. Here, many of the illustrating examples are the Lorentzian manifolds which later serve as spacetime models. This has the twofold purpose of making the physics forthcoming in the second part relatable, and the mathematics learnt in the first part less dry. The book uses the modern coordinate-free language of semi-Riemannian geometry. Nevertheless, to familiarise the reader with the useful tool of coordinates for computations, and to bridge the gap with the physics literature, the link to coordinates is made through exercises, and via frequent remarks on how the two languages are related.In the second part, the focus is on physics, covering essential material of the 20th century spacetime-based view of gravity: energy-momentum tensor field of matter, field equation, spacetime examples, Newtonian approximation, geodesics, tests of the theory, black holes, and cosmological models of the universe.Prior knowledge of differential geometry or physics is not assumed. The book is intended for self-study, and the solutions to the (over 200) exercises are included.
商品描述(中文翻譯)
本書旨在為高年級本科數學學生提供廣義相對論的數學呈現(即基於時空幾何的引力理論)。數學家將會發現時空物理以他們熟悉的定義-定理-證明格式呈現。給出的物理概念的精確數學定義有助於避免陷阱,特別是在描述與日常經驗相悖的現象的時空物理背景下。
在第一部分,從零開始發展平滑流形的微分幾何,這是呈現基於時空的引力理論所需的。在這裡,許多示例都是洛倫茲流形,這些流形後來作為時空模型。這有助於使第二部分的物理內容更具關聯性,並使第一部分學到的數學不那麼枯燥。本書使用現代無坐標的半黎曼幾何語言。然而,為了讓讀者熟悉坐標這一計算的有用工具,並彌合與物理文獻之間的差距,通過練習和對兩種語言之間關係的頻繁說明來建立與坐標的聯繫。
在第二部分,重點放在物理上,涵蓋20世紀基於時空的引力觀的基本材料:物質的能量-動量張量場、場方程、時空示例、牛頓近似、測地線、理論的測試、黑洞以及宇宙的宇宙學模型。不假設讀者具備微分幾何或物理的先前知識。本書旨在自學,並包含(超過200道)練習的解答。