Introduction into General Theory of Relativity
- 4.4
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Course Summary
Explore the fundamental principles of General Relativity and its applications in astrophysics, gravitation waves and cosmology.Key Learning Points
- Understand the mathematical and physical principles of General Relativity
- Apply the principles of General Relativity in astrophysics and cosmology
- Learn about the latest research and discoveries in gravitational waves
Job Positions & Salaries of people who have taken this course might have
- Astrophysicist
- USA: $120,000
- India: ₹1,800,000
- Spain: €60,000
- Cosmologist
- USA: $110,000
- India: ₹1,600,000
- Spain: €55,000
- Gravitational Wave Researcher
- USA: $130,000
- India: ₹2,000,000
- Spain: €65,000
Related Topics for further study
Learning Outcomes
- Understand the principles of General Relativity
- Apply the principles of General Relativity in astrophysics and cosmology
- Learn about the latest research and discoveries in gravitational waves
Prerequisites or good to have knowledge before taking this course
- A basic understanding of calculus and physics
- Familiarity with special relativity
Course Difficulty Level
AdvancedCourse Format
- Online
- Self-paced
Similar Courses
- Introduction to Astrophysics
- Cosmology and Particle Physics
Related Education Paths
Notable People in This Field
- Albert Einstein
- Stephen Hawking
Related Books
Description
General Theory of Relativity or the theory of relativistic gravitation is the one which describes black holes, gravitational waves and expanding Universe. The goal of the course is to introduce you into this theory. The introduction is based on the consideration of many practical generic examples in various scopes of the General Relativity. After the completion of the course you will be able to solve basic standard problems of this theory. We assume that you are familiar with the Special Theory of Relativity and Classical Electrodynamics. However, as an aid we have recorded several complementary materials which are supposed to help you understand some of the aspects of the Special Theory of Relativity and Classical Electrodynamics and some of the calculational tools that are used in our course. Also as a complementary material we provide the written form of the lectures at the website: https://math.hse.ru/generalrelativity2015
Outline
- General Covariance
- About the University
- Introduction
- General covariance
- Сonstant linear acceleration
- Transition to the homogeneously accelerating reference frame (or system) in Minkowski space–time
- Transition to the homogeneously accelerating reference frame in Minkowski space–time (part 2)
- Geodesic equation
- Christoffel symbols
- About University
- Rules on the academic integrity in the course
- Covariant differential and Riemann tensor
- Tensors
- Covariant differentiation
- Parallel transport
- Covariant differentiation(part 2)
- Locally Minkowskian Reference System (LMRS)
- Curvature or Riemann tensor
- Properties of Riemann tensor
- Tensors in flat space-time(part 1)
- Tensors in flat space-time(part 2)
- Einstein-Hilbert action and Einstein equations
- Einstein–Hilbert action
- Einstein equations
- Matter energy–momentum (or stress-energy) tensor
- Examples of matter actions
- The least action (or minimal action) principle (part 1)
- The least action principle (part 2)
- Schwarzschild solution
- Schwarzschild solution
- Schwarzschild solution(part 2)
- Gravitational radius
- Schwarzschild coordinates
- Eddington–Finkelstein coordinates
- Penrose-Carter diagrams
- Penrose–Carter diagrams
- Kruskal–Szekeres coordinates
- Penrose–Carter diagram for the Schwarzschild black hole
- Penrose–Carter diagram for the Schwarzschild black hole (part 2)
- Classical tests of General Theory of Relativity
- Killing vectors and conservation laws
- Test particle motion on Schwarzschild black hole background
- Test particle motion on Schwarzschild black hole background(part 2)
- Mercury perihelion precession
- Light ray deviation in the vicinity of the Sun
- Interior solution and Kerr's solution
- Energy–momentum tensor of a perfect relativistic fluid
- Interior solution.
- Interior solution (part 2)
- Kerr’s rotating black hole
- Collapse into black hole
- Oppenheimer–Snyder collapse
- Penrose–Carter diagram for the Oppenheimer– Snyder collapsing solution
- Hints on Hawking radiation
- Black hole horizon creation
- Gravitational waves
- Energy–momentum pseudo–tensor for gravity
- Weak field approximation
- Free gravitational waves
- Gravitational radiation
- Gravitational radiation by moving massive bodies
- Intensity of the radiation
- Shock gravitational wave or Penrose parallel plane wave
- Properties of the Penrose parallel plane wave
- Green functions
- Averages
- Friedman-Robertson-Walker cosmology
- Homogeneous three–dimensional spaces
- Friedmann–Robertson–Walker metric
- Homogeneous isotropic cosmological solutions
- Anisotropic Kasner cosmological solution
- Cosmological solutions with non-zero cosmological constant
- De Sitter and anti-de Sitter
- Geometry of the de Sitter space–time
- Metric of the de Sitter space–time
- Penrose–Carter diagram for the de Sitter space–time
- Poincare' patches for the de Sitter space–time
- Geometry of the anti–de Sitter space–time
- Metric of the anti–de Sitter space–time
- Penrose–Carter diagram of the anti–de Sitter space–time
- Poincare' patch of the anti–de Sitter space–time
Summary of User Reviews
Read reviews for the General Relativity course on Coursera. Users have rated the course highly and many appreciated the clear explanations provided. However, some found the content challenging and the course pace too slow.Key Aspect Users Liked About This Course
Clear explanationsPros from User Reviews
- Well-structured and organized
- Great visuals and animations
- In-depth coverage of the topic
Cons from User Reviews
- Challenging content
- Slow pace
- Some technical issues with videos
Emil Akhmedov
4.4 Raiting
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