In general relativity, the metric tensor (in this context often abbreviated to simply the metric) is the fundamental object of study. It may loosely be thought of as a generalization of the gravitational potential of Newtonian gravitation. The metric captures all the geometric and causal structure of spacetime, being used to define notions such as time, distance, volume, curvature, angle, and separation of the future and the past. (Wikipedia).
What is General Relativity? Lesson 68: The Einstein Tensor
What is General Relativity? Lesson 68: The Einstein Tensor The Einstein tensor defined! Using the Ricci tensor and the curvature scalar we can calculate the curvature scalar of a slice of a manifold using the Einstein tensor. Please consider supporting this channel via Patreon: https:/
From playlist What is General Relativity?
The Maths of General Relativity (4/8) - Metric tensor
In this series, we build together the theory of general relativity. This fourth video focuses on the notion of metric tensor, its relations to the Christoffel symbols, and physical distances. For more videos, subscribe to the YouTube channel : https://www.youtube.com/ScienceClicEN And if
From playlist The Maths of General Relativity
What is General Relativity? Lesson 48: Ricci tensor and conformal transformations
What is General Relativity? Lesson 48: Ricci tensor and conformal transformations We introduce the Ricci tensor, curvature scalar, and begin the difficult derivation of the Weyl tensor. Please consider supporting this channel via Patreon: https://www.patreon.com/XYLYXYLYX and discussin
From playlist What is General Relativity?
What is General Relativity? Lesson 8: Intro to the metric connection and the induced metric.
This lesson is an introduction to the concept of the metric connection followed by a long exercise in classical differential geometry. It is a long lesson because I complete a full example: the derivation of the metric of the "glome" induced by the Euclidean metric of 4-dimensional space.
From playlist What is General Relativity?
What is General Relativity? Lesson 52: Scalar Curvature Part I
What is General Relativity? Lesson 52: Scalar Curvature Part I This is the first of a few lectures about the Scalar Curvature and its interpretation. The goal is to get us to a point where we can have an interpretation of the Einstein Tensor and therefore an interpretation of the Einstein
From playlist What is General Relativity?
What is General Relativity? Lesson 67: Pullback example and introduction to metric equivalence.
In this lesson we cover two topics: the pullback of a simple metric from R^2 to S^1. Then we explore the idea of using a coordinate transformation on S^1 to show that two metric's on S^1 are actually the same. Note: at 37:00, on the third line, I wrote "dx^0 @ dx^2" which is a mistake. It
From playlist What is General Relativity?
What is General Relativity? Lesson 56 - Scalar curvature Part 5: More Riemann Normal Coordinates
What is General Relativity? Lesson 56 - Scalar curvature Part 5: More Riemann Normal Coordinates In this lecture we re-work the Riemann Normal Coordinate formalism from the point of view of a coordinate transformation and leaning on the Einstein Equivalence Principle. We also point out wh
From playlist What is General Relativity?
What is General Relativity? Lesson 16: The metric connection
We finally derive the metric connection using the CFREE algebra and a conversion to the Catalog's COMP expression! Errata: I never did demonstrate that [X,Y] was a vector, so you might have to look that fact up yourself. Also I called it the "Lie Bracket" but it should be called the "Lie
From playlist What is General Relativity?
What is General Relativity? Lesson 39: The curvature - formal introduction
What is General Relativity? Lesson 39: The curvature - formal introduction The Riemann Curvature Tensor is presented as a strictly formal object. Take note of an error captured by viewer "Endevor" in the comments. I may redo this video soon to fix it! Please consider supporting this chan
From playlist What is General Relativity?
Einstein's General Theory of Relativity | Lecture 9
Lecture 9 of Leonard Susskind's Modern Physics concentrating on General Relativity. Recorded November 17, 2008 at Stanford University. This Stanford Continuing Studies course is the fourth of a six-quarter sequence of classes exploring the essential theoretical foundations of modern phy
From playlist Lecture Collection | Modern Physics: Einstein's Theory
Einstein's final work is STILL unfinished. Here’s what it means.
To try everything Brilliant has to offer FREE for a full 30 days, visit http://brilliant.org/ParthG/. The first 200 of you will get 20% off Brilliant’s annual premium subscription. This is Einstein's final contribution to physics... and unfortunately it was left unfinished. Also, a huge
From playlist Relativity by Parth G
Lec 08. Einstein's General Relativity and Gravitation: General Relativity 4
UCI Physics 255 Einstein's General Relativity and Gravitation (Spring 2014) Lec 08. Einstein's General Relativity and Gravitation -- General Relativity -- Part 4 View the complete course: http://ocw.uci.edu/courses/einsteins_general_relativity_and_gravitation.html Instructor: Herbert W. Ha
From playlist Einstein's General Relativity and Gravitation
Generalized Geometry for String Theory - B. Zwiebach - 12/10/2013
A conference celebrating the 50th anniversary of quarks honoring Murray Gell-Mann was held at Caltech on December 9-10, 2013. For more information, visit: http://hep.caltech.edu/gm/
From playlist String Theory - Prof. Zwiebach & Susskind
Generation and imprints of primordial gravitational waves (Lecture 1) by Daniel Figueroa
PROGRAM PHYSICS OF THE EARLY UNIVERSE (HYBRID) ORGANIZERS: Robert Brandenberger (McGill University, Canada), Jerome Martin (IAP, France), Subodh Patil (Leiden University, Netherlands) and L. Sriramkumar (IIT - Madras, India) DATE: 03 January 2022 to 12 January 2022 VENUE: Online and Ra
From playlist Physics of the Early Universe - 2022
Lec 10. Einstein's General Relativity and Gravitation: General Relativity 6
UCI Physics 255 Einstein's General Relativity and Gravitation (Spring 2014) Lec 10. Einstein's General Relativity and Gravitation -- General Relativity -- Part 6 View the complete course: http://ocw.uci.edu/courses/einsteins_general_relativity_and_gravitation.html Instructor: Herbert W. Ha
From playlist Einstein's General Relativity and Gravitation
Tensor Calculus Lecture 7b: Relative Tensors
This course will eventually continue on Patreon at http://bit.ly/PavelPatreon Textbook: http://bit.ly/ITCYTNew Errata: http://bit.ly/ITAErrata McConnell's classic: http://bit.ly/MCTensors Table of Contents of http://bit.ly/ITCYTNew Rules of the Game Coordinate Systems and the Role of Te
From playlist Introduction to Tensor Calculus
14. Linearized gravity I: Principles and static limit.
MIT 8.962 General Relativity, Spring 2020 Instructor: Scott Hughes View the complete course: https://ocw.mit.edu/8-962S20 YouTube Playlist: https://www.youtube.com/playlist?list=PLUl4u3cNGP629n_3fX7HmKKgin_rqGzbx Solving the Einstein field equation by linearizing around a flat background.
From playlist MIT 8.962 General Relativity, Spring 2020
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From playlist Science Unplugged: General Relativity