Einstein's Field Equations of General Relativity Explained
Why Physics Stack Exchange recommends it
Physics Stack Exchange users link it as a visual introduction to GR concepts like Christoffel symbols and curvature tensors, especially for newcomers who find the math abstract.
Recommended by 3 people across 3 different months, 2017 to 2023.
What it is
An animated, roughly half-hour visual walkthrough of general relativity by Eugene Khutoryansky. It builds up Christoffel symbols and the Riemann curvature tensor, then explains each term in Einstein's field equations using geometric animations and narration.
What people said
Recommends gen-ℤ ready to perish · 2017-12 · Physics Stack Exchange · on “How does one describe how a basis vector changes through space using the Christoffel symbols?”
I have been watching this video [this video] , which explains in fair detail what each of the terms in Einstein’s field equation represents. The portion I linked explains the tensor object ${\Gamma^\alpha}_{\beta\gamma}$, which I believe is also called a Christoffel symbol. To summarize, if spacetime is curved or if a coordinate system is curved, then the basis vector in a particular dimension is not necessarily constant throughout space. The change in the basis vector along a dimension can be described as a linear combination of all the coordinate system’s basis vectors. [LINK] [LINK] The video indicates that for the tensor object ${\Gamma^\alpha}_{\beta\gamma}$, $\alpha$ indicates which basis v
Recommends Mauro Giliberti · 2020-09 · Physics Stack Exchange · on “Light rays curved path in General Relativity”
Welcome to Physics SE! First of all, if you don't understand GR at all, I suggest you look up something online: there are a lot of "GR 101" videos, for example Eugene Khutoryansky [this video] or PBS SpaceTime [LINK] , that provide a very visual understanding. Secondly, as the comment by G. Smith pointed out, that kind of image can be very misleading if you don't know the subject well. The reason for this is that, in GR, there is no 2D fabric to be bent: the whole 4D spacetime is. Even if this is not a perfect representation as it obviously only shows only a 3D projected image , you may get a better understanding of what's going on in GR taking a look at pictures like this GIF [LINK] . Lastly, yo
Recommends user291777 · 2021-03 · Physics Stack Exchange · on “Why can curved spacetime be locally a Minkowskian spacetime?”
When you use calculus a curve is approximated by small straight lines.You have to do this for curved space.Look at the second minute of this video [this video]
Cites user315366 · 2021-10 · Physics Stack Exchange · on “How to compute and interpret Schwartzchild black-hole metric line element $ds$ in Cartesian coordinates?”
@ Paul But there is another major thing that I am still unclear about, it relates to the method for finding the line of geodesics vectorially. It is explained in [this video] (around 0:45) and it seems that he is implying that he can manage to find the geodesic path in this way, without involving the Christoffer symbols. Do you foresee any problems with the method in the video for calculating geodesic path? Thank you.
Cites Yukterez · 2023-01 · Physics Stack Exchange · on “Is there no curvature due to mass when travelling along a sphere outside a black hole?”
For what direction curves into which for the specified local observer in your coordinates you need the Riemann [this video] curvature tensor, see here [LINK] at Output 4 (in that link the indices {1,2,3,4} are {t,r,θ,φ} so they start with 1, not 0). That depends on the motion of the local observers, therefore its components are different in different coordinates for the same metric.