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Introduction into General Theory of Relativity

Approx. 29 hours to complete

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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

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

Advanced

Course 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 explanations

Pros 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

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