Relating Metric Tensor to Gravity | Tensor Calculus Ep. 16

Today I show how in the Newtonian limit, we're able to relate the metric tensor to the gravitational potential. We do this by imposing a static weak field metric, and see how this affects the geodesic equation. This will be one of many useful pieces of information we can use to argue what Einstein's Field Equations will be.

This series is based off of the book "Tensor Calculus for Physics" by Dwight Neuenschwander

0:00 Introduction
1:50 Geodesic Equation
3:20 Newtonian Limit
5:40 Static Weak-Field Metric
12:30 Comparing Geodesic Equation with Free Fall Equation
15:05 Relating the SWF Metric to Gravitational Potential
15:42 Final Comments and Conclusion

[srijan]

Do I understand any of it:No
Am I watching it shamelessly still: hell yeah

[helms]

You know the rules boys—you see “tensor” and hit the like button.

I am only here because I am trying to learn the stress tensor for materials and structures—this helps with my laminates course.

[meowwwww]

#freedomforandrew
#releaseandrewfromthebasement

[LavenderTown]

Hartle: I think I can explain Tensors/GR fairly well.
Andrew: hold my beer...

[maureendotson]

Back down to #86 😩. Great video Andrew! ~ Mom💕

[thomassenecal]

Glad I can learn some smart stuff after getting out of my intro to engineering class

[AdityaKumar-ijok]

Learning with ads is like learnings with classmates

[kevingrant]

What is this 2 tensor calculus video in a matter of a couple weeks

[narfwhals]

PBS spacetime: does time cause gravity?
Andrew: but here's why.

[juijani]

Andrew and papa are like yin and yang, one uses the (+ - - - ) metric signature being in the basement while the other ( - + + +) being in the attic/loft! Both must also coexist!!

[Airsofter]

Great video as always!

I was reminded when I was the formula for the Christoffel symbols (at 4:56 and later) in this video how I always felt kind of uncomfortable that you need to assume the levi-civita connection in GR. However, I discovered about a year ago there is a more natural reason for this.

If you write the Einstein Hilbert action in terms of the metric and generic connection coefficients (i.e. you write out the Ricci scalar in terms of the connection coefficients, but then don't expand those using the equation 4:56 as you usually would), you can treat the connection coefficients as a separate field. The equations of motion that occur from varying this field imply the same identities you get by assuming the levi-civita connection, which you can then plug back into your action to get the usual Einstein Hilbert action that depends on the metric and its derivatives. This is called the Palatini formulation of GR and is covered quite nicely in the book Gravity and String by Ortin (Along with other formulations such as how you can get GR with only torsion and no curvature). You actually have to use the Palatini formulation if you want to consider fermions moving in curved space, as it turns out they cause local torsion taking you away from the Levi-Civita connection!

Sorry for the kinda technical and long comment, but I think it's awesome and really changed how I think of GR!

[johubify]

I dont even understand basic Tensor math, what am I doing

[gurleensingh]

You like everyone's comment like this one too.If you don't like, I will still be here.☺☺☺

[anishparulekar]

Was the winner for the giveaway announced?

[mohammadtarshihi]

I’m planning on starting with the tensor calc series tomorrow, so thanks for that addition Andrew.

[marshalltaylor]

First is the worst, second is the best🗣

[sameer]

Andrew, c'mon when are you going to watch Endgame???!

[dibyojyotibhattacharjee]

Hey Andrew, can u do a series in which you solve "good" physics problems from various books?

[Eigenbros]

This is a work of beauty 🔥 Great explanation, Andrew. We're going to have to watch all of these from the beginning now.

[juijani]

Ahhh!!! I forget you're a particle/nuclear physicist and then suddenly 6:15 happened with the Minkowski metric!
(i don't know why i sometimes confuse myself with particle and nuclear physics...lol)