Einstein Field Equations - for beginners!
Why Physics Stack Exchange recommends it
Physics Stack Exchange askers cite it as the tutorial they are following when they get stuck on specific steps, such as coordinate transformations, the metric tensor and a commutator identity.
Recommended by 1 people across 1 different months, 2017 to 2020.
What it is
A two-hour whiteboard-style lecture by DrPhysicsA that builds up to Einstein's field equations from scratch. It covers the metric tensor, Christoffel symbols, the Ricci curvature tensor, the curvature scalar, the stress-energy-momentum tensor and the cosmological constant.
What people said
Recommends S. Rotos · 2017-09 · Physics Stack Exchange · on “Commutator question”
I'm watching this video going through a non-rigorous explanation of the Einstein field equations: [this video] At around 1:17:50 [this video] he shows an identity involving the commutator of what looks like the differential operator and a function of $x$. This is what I don't understand. It looks weird to begin with, having just the operator there instead of an actual derivative of a function. He then comes up with the variable $v$ so that there is something to apply the operator to. On the left hand side he writes $v$ to the right and then says that there is now a derivative of a product. But how is that? If the differential operator is applied to $v$, why is the left hand side not the derivative of
Cites Lincon Ribeiro · 2019-01 · Physics Stack Exchange · on “General Relativity: Exchanging a field with its infinitesimal components on metric tensor”
On a youtube video about Einstein's field equations, the author writes the following equation ( [this video] ): $$d\phi=\sum_{n} \frac{\partial \phi}{\partial x^n} dx^n\tag{1}$$ Where $d\phi$ is the gradient of a tensor field. After some explanations regarding metrics, he changes equation (1) to ( [this video] ): $$dx^m=\frac{\partial x^m}{\partial y^r}dy^r\tag{2}$$ where the summation over $r$ is implied. Why this can be done? I don't understand the change from $d\phi$ to $dx^m$ .
Cites I'm a lightbulb · 2020-06 · Physics Stack Exchange · on “I don't know why i can't use this equation (in the pic) in flatspace, I'm learning general relativity (metric tensor)”
Because im watching a tutorial form Youtube [this video] if you see 52:01, he says that in a flat space, the metric tensor must be changed to the Kronecker Delta, Why?
Cites l3utterfly · 2020-11 · Physics Stack Exchange · on “Vector transformation derived from partial derivatives”
I am studying the lecture on general relativity for beginners here: [this video] I was able to follow the steps up until this point (33:18 in the video). During the deriving of the metric tensor, he is talking about how the vector transforms in a change of basis. He derived a formula using a gradient formula with partial derivatives by simply replacing the gradient by a vector. [LINK] The circled formula is what he derived from the boxed formula above. As I understand, X and Y here are frames of reference (rather than coordinates). How is the partial derivative of Y with respect to X obtained?