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지금 바로 시작해 나만의 일정에 따라 학습을 진행하세요.

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일정에 따라 마감일을 재설정합니다.

고급 단계

영어

자막: 영어

100% 온라인

지금 바로 시작해 나만의 일정에 따라 학습을 진행하세요.

유동적 마감일

일정에 따라 마감일을 재설정합니다.

고급 단계

영어

자막: 영어

강의 계획 - 이 강좌에서 배울 내용

1
완료하는 데 3시간 필요

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.

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7 videos (Total 75 min), 1 quiz
7개의 동영상
General covariance12m
Сonstant linear acceleration16m
Transition to the homogeneously accelerating reference frame (or system) in Minkowski space–time8m
Transition to the homogeneously accelerating reference frame in Minkowski space–time (part 2)13m
Geodesic equation8m
Christoffel symbols14m
2
완료하는 데 4시간 필요

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.

...
9 videos (Total 124 min), 1 quiz
9개의 동영상
Covariant differentiation15m
Parallel transport10m
Covariant differentiation(part 2)9m
Locally Minkowskian Reference System (LMRS)16m
Curvature or Riemann tensor15m
Properties of Riemann tensor13m
Tensors in flat space-time(part 1)21m
Tensors in flat space-time(part 2)13m
3
완료하는 데 4시간 필요

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.

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6 videos (Total 86 min), 1 quiz
6개의 동영상
Einstein equations19m
Matter energy–momentum (or stress-energy) tensor15m
Examples of matter actions17m
The least action (or minimal action) principle (part 1)11m
The least action principle (part 2)12m
4
완료하는 데 3시간 필요

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.

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5 videos (Total 55 min), 1 quiz
5개의 동영상
Schwarzschild solution(part 2)17m
Gravitational radius6m
Schwarzschild coordinates7m
Eddington–Finkelstein coordinates11m
4.6
33개의 리뷰Chevron Right

Introduction into General Theory of Relativity의 최상위 리뷰

대학: 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.

대학: 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.

강사

Avatar

Emil Akhmedov

Associate Professor
Faculty of Mathematics

국립 연구 고등 경제 대학 정보

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 communicamathematics, engineering, and more. Learn more on www.hse.ru...

자주 묻는 질문

  • 강좌에 등록하면 바로 모든 비디오, 테스트 및 프로그래밍 과제(해당하는 경우)에 접근할 수 있습니다. 상호 첨삭 과제는 이 세션이 시작된 경우에만 제출하고 검토할 수 있습니다. 강좌를 구매하지 않고 살펴보기만 하면 특정 과제에 접근하지 못할 수 있습니다.

  • 수료증을 구매하면 성적 평가 과제를 포함한 모든 강좌 자료에 접근할 수 있습니다. 강좌를 완료하면 전자 수료증이 성취도 페이지에 추가되며, 해당 페이지에서 수료증을 인쇄하거나 LinkedIn 프로필에 수료증을 추가할 수 있습니다. 강좌 콘텐츠만 읽고 살펴보려면 해당 강좌를 무료로 청강할 수 있습니다.

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