- 来自www.coursera.org
Introduction into General Theory of Relativity
课程
en
英语
48 时
此内容评级为 0/5
- 自定进度
- 免费获取
- 收费证书
- 12 序列
- 等级 高级
课程详情
教学大纲
- Week 1 - General Covariance
To start with, we recall the basic notions of the Special Theory of Relativity. We explain that Minkwoskian coordinates in flat space-time correspond to inertial observers. Then we continue with transformations to non-inertial reference systems in flat space-t... - Week 2 - Covariant differential and Riemann tensor
We start with the definition of what is tensor in a general curved space-time. Then we define what is connection, parallel transport and covariant differential. We show that for Riemannian manifolds connection coincides with the Christoffel symbols and geodesi... - Week 3 - Einstein-Hilbert action and Einstein equations
We start with the explanation of how one can define Einstein equations from fundamental principles. Such as general covariance, least action principle and the proper choice of dynamical variables. Namely, the role of the latter in the General Theory of Relativ... - Week 4 - Schwarzschild solution
With this module we start our study of the black hole type solutions. We explain how to solve the Einstein equations in the simplest settings. We find perhaps the most famous solution of these equations, which is referred to as the Schwarzschild black hole. We... - Week 5 - Penrose-Carter diagrams
We start with the definition of the Penrose-Carter diagram for flat space-time. On this example we explain the uses of such diagrams. Then we continue with the definition of the Kruskal-Szekeres coordinates which cover the entire black hole space-time. With th... - Week 6 - Classical tests of General Theory of Relativity
We start with the definition of Killing vectors and integrals of motion, which allow one to provide conserving quantities for a particle motion in Schwarzschild space-time. We derive the explicit geodesic equation for this space-time. This equation provides a ... - Week 7 - Interior solution and Kerr's solution
We start with the definition of the so called perfect fluid energy-momentum tensor and with the description of its properties. We use this tensor to derive the so called interior solution of the Einstein equations, which provides a simple model of a star in th... - Week 8 - Collapse into black hole
We start with the derivation of the Oppenheimer-Snyder solution of the Einstein equations, which describes the collapse of a star into black hole. We derive the Penrose-Carter diagram for this solution. We end up this module with a brief description of the ori... - Week 9 - Gravitational waves
With this module we start our study of gravitational waves. We explain the important difference between energy-momentum conservation laws in the absence and in the presence of the dynamical gravity. We define the gravitational energy-momentum pseudo-tensor. Th... - Week 10 - Gravitational radiation
In this module we show how moving massive bodies create gravitational waves in the linearized approximation. Then we continue with the derivation of the exact shock gravitational wave solutions of the Einstein equations. We describe their properties.To help t... - Week 11 - Friedman-Robertson-Walker cosmology
With this module we start our discussion of the cosmological solutions. We define constant curvature three-dimensional homogeneous spaces. Then we derive Friedman-Robertson-Walker cosmological solutions of the Einstein equations. We describe their properties. ... - Week 12 - Cosmological solutions with non-zero cosmological constant
In this module we derive constant curvature de Sitter and anti de Sitter solutions of the Einstein equations with non-zero cosmological constant. We describe the geometric and causal properties of such space-times and provide their Penrose-Carter diagrams. We ...
先决条件
没有。
讲师
Emil Akhmedov
Associate Professor
Faculty of Mathematics
编辑
莫斯科国立研究大学 "高等经济学院"（EHESE）于 1992 年在俄罗斯经济学家的倡议下成立。
自 2001 年以来，它一直是一所国立大学，最初由经济发展部监管，自 2008 年以来，它一直是直属于俄罗斯联邦政府的高等教育和研究机构。经过校际竞赛，该校于 2009 年被授予俄罗斯国立研究型大学的地位。
它在国际上被称为高等经济学院（HSE）。
除莫斯科外，该校还在圣彼得堡、下诺夫哥罗德和彼尔姆设有三个附属校区。
在 QS 世界大学排名中，该校经常名列世界最佳大学前 100 名，在俄罗斯名列第二4。
平台
Coursera是一家数字公司，提供由位于加利福尼亚州山景城的计算机教师Andrew Ng和达芙妮科勒斯坦福大学创建的大型开放式在线课程。
Coursera与顶尖大学和组织合作，在线提供一些课程，并提供许多科目的课程，包括：物理，工程，人文，医学，生物学，社会科学，数学，商业，计算机科学，数字营销，数据科学 和其他科目。
此内容评级为 4.5/5
(没有评论)此内容评级为 4.5/5
(没有评论)完成这个资源，写一篇评论