课程信息
4.6
85 个评分
29 个审阅
100% 在线

100% 在线

立即开始,按照自己的计划学习。
可灵活调整截止日期

可灵活调整截止日期

根据您的日程表重置截止日期。
高级

高级

完成时间(小时)

完成时间大约为50 小时

建议:12 weeks of study, 4-6 hours per week...
可选语言

英语(English)

字幕:英语(English)
100% 在线

100% 在线

立即开始,按照自己的计划学习。
可灵活调整截止日期

可灵活调整截止日期

根据您的日程表重置截止日期。
高级

高级

完成时间(小时)

完成时间大约为50 小时

建议:12 weeks of study, 4-6 hours per week...
可选语言

英语(English)

字幕:英语(English)

教学大纲 - 您将从这门课程中学到什么

1
完成时间(小时)
完成时间为 3 小时

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-time. We show that non-inertial observers correspond to curved coordinate systems in flat space-time. In particular, we describe in grate details Rindler coordinates that correspond to eternally homogeneously accelerating observers. This shows that our Nature allows many different types of metrics, not necessarily coincident with the Euclidian or Minkwoskain ones. We explain what means general covariance. We end up this module with the derivation of the geodesic equation for a general metric from the least action principle. In this equation we define the Christoffel symbols....
Reading
7 个视频 (总计 75 分钟), 1 个测验
Video7 个视频
General covariance12分钟
Сonstant linear acceleration16分钟
Transition to the homogeneously accelerating reference frame (or system) in Minkowski space–time8分钟
Transition to the homogeneously accelerating reference frame in Minkowski space–time (part 2)13分钟
Geodesic equation8分钟
Christoffel symbols14分钟
2
完成时间(小时)
完成时间为 4 小时

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 geodesic equations acquire a clear geometric meaning. We end up with the definition of the Riemann tensor and the description of its properties. We explain how Riemann tensor allows to distinguish flat space-time in curved coordinates from curved space-times. For this module we provide complementary video to help students to recall properties of tensors in flat space-time. ...
Reading
9 个视频 (总计 124 分钟), 1 个测验
Video9 个视频
Tensors9分钟
Covariant differentiation15分钟
Parallel transport10分钟
Covariant differentiation(part 2)9分钟
Locally Minkowskian Reference System (LMRS)16分钟
Curvature or Riemann tensor15分钟
Properties of Riemann tensor13分钟
Tensors in flat space-time(part 1)21分钟
Tensors in flat space-time(part 2)13分钟
3
完成时间(小时)
完成时间为 3 小时

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 Relativity is played by the metric tensor of space-time. Then we derive the Einstein equations from the least action principle applied to the Einstein-Hilbert action. Also we define the energy-momentum tensor for matter and show that it obeys a conservation law. We describe the basic generic properties of the Einstein equations. We end up this module with some examples of energy-momentum tensors for different sorts of matter fields or bodies and particles.To help understanding this module we provide complementary video with the explanation of the least action principle in the simplest case of the scalar field in flat two-dimensional space-time....
Reading
6 个视频 (总计 86 分钟), 1 个测验
Video6 个视频
Einstein equations19分钟
Matter energy–momentum (or stress-energy) tensor15分钟
Examples of matter actions17分钟
The least action (or minimal action) principle (part 1)11分钟
The least action principle (part 2)12分钟
4
完成时间(小时)
完成时间为 3 小时

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 formulate the Birkhoff theorem. We end this module with the description of some properties of this Schwarzschild solution. We provide different types of coordinate systems for such a curved space-time. ...
Reading
5 个视频 (总计 55 分钟), 1 个测验
Video5 个视频
Schwarzschild solution(part 2)17分钟
Gravitational radius6分钟
Schwarzschild coordinates7分钟
Eddington–Finkelstein coordinates11分钟
4.6
29 个审阅Chevron Right

热门审阅

创建者 PPSep 24th 2017

Best Course for Physics Enthusiasts. It is a must for those who are interested in theoretical or mathematical physics. I really enjoyed the course though it was tough.

创建者 VUFeb 2nd 2017

Excellent course, and quite intensive mathematically. One will be well placed for a graduate level course on General relativity upon completing this.

讲师

Avatar

Emil Akhmedov

Associate Professor
Faculty of Mathematics

关于 National Research University Higher School of Economics

National Research University - Higher School of Economics (HSE) is one of the top research universities in Russia. Established in 1992 to promote new research and teaching in economics and related disciplines, it now offers programs at all levels of university education across an extraordinary range of fields of study including business, sociology, cultural studies, philosophy, political science, international relations, law, Asian studies, media and communications, IT, mathematics, engineering, and more. Learn more on www.hse.ru...

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