12. The Einstein field equation.

MIT 8.962 General Relativity, Spring 2020
Instructor: Scott Hughes

The Einstein curvature tensor, a variation on the Ricci curvature, defined so that it has vanishing covariant divergence.  Using this tensor, we at last build a field theory for spacetime, motivating the Einstein field equation by arguing how to generalize a gravitational field equation to relativity.

License: Creative Commons BY-NC-SA

[WiperTF]

1:17:09 such a cool highlight I wanted to come back to. "Spacetime is HARD TO BEND."

[emiliabrambilla]

Fantstic! thank you prof Scott for helping us discovering Einstein thougths

[AkamiChannel]

Hey, great job! You're an amazing teacher

[jacobvandijk]

Once upon a time Einstein took a balloon and observed it carefully. After a few minutes he realised that the air-molecules in the balloon had an average velocity and thus the inside of the balloon had to have a certain energy-density (Joule/Volume). He also realised that these molecules kept bumping into the surface of the balloon. Thus the surface experienced a pressure from within, called stress (Newton/Area). All these stresses can be decomposed in normal and shear stresses. That's what he had learned at the ETH in Zurich. But he wasn't satisfied yet, because his balloons deflated after some time. Giving this some thought he came up with this great idea that there has to be a flow of particles through the surface! This kind of dynamics is introduced in physics through momentum and flux, he remembered. Well, that's easy, Einstein thought. Momentum-density = energy-density / velocity, and energy-flux = energy-density x velocity. Man, that's great, Einstein yelled. Now I've got all the components of my Stress-Energy-Tensor! Then he grabbed a balloon and popped it, lol.

[finalfantasy]

@1:15:29 "I can't erase this equation. It's too beautiful" . LoL

[eytansuchard]

Scott: Thank you for this lecture. My professor was Nathan Rosen from EPR. I like your lecture more.

[johnpcourter]

So, in theory Einstein's relativity is solved to be a law of numerical approximation relativity by solving Time and Pi as the divergence-free, two index tenser, as pair?

[Mr_ST_]

Big thanks n respect to u sir from India

[trippmoss]

Hello, Professor Hughes! I have some praise, and one question:

Firstly, absolutely wonderful lecture. This is the first content I have found which approaches the topic with enough mathematical rigor to be applicable, but still motivates the elegance of the theory. Thank you for your content!

Secondly- most derivations I find in GR use the weak field approximation, with the perturbative “h” terms. Is this one of the only ways to reach solvable equations? What does this mean for the validity of our results, and are most/all of the results of GR simply an approximation?

[riemann]

couldn't understand GAMMA_0_0_0 = 0 @ 35:55 ... where did this come from

[NothingMaster]

You mean: ‘The Einstein Field Equation(S)’, right?

[pacajalbert]

Jedna planéta od povedala napi sa vody aby si mohol lietať ďalej kde som videl iní vesmír 🌌 ne ten kde som bol ten sami mali chlapec 🧒

[TheTwick]

“Hey, doc. You missed a nu.” Sorry. I was just pretending to be one of your brilliant students. It’s just not the same, is it?

[MasterCivilEngineering]

Step by step video solutions of engineering questions

[iRReligious]

Oh is it was a COVID time? That's why empty classroom?🤣