General Relativity Lecture 3
Why Physics Stack Exchange recommends it
Physics Stack Exchange users cite it when asking about or explaining Riemannian geometry foundations of GR, such as normal coordinates, covariant derivatives and curvature.
Recommended by 1 people across 1 different months, 2015 to 2025.
What it is
Third lecture in Leonard Susskind's Stanford general relativity course, recorded in October 2012 as part of the Theoretical Minimum series. He continues Riemannian geometry and uses it as the foundation for Einstein's theory, including the existence of locally flat coordinates at a point.
What people said
Recommends tomdodd4598 · 2020-07 · Physics Stack Exchange · on “Argument for existence of normal coordinates at a given point”
I've been recently been going back over the basics of GR, differential geometry in particular. I was watching one of Susskind's lectures and did not understand the argument made here [this video] (26:33 - 35:40). In short, the argument goes as follows (I think): we have some generic metric ${ g }_{ m n }^{ ' }\left( y \right)$ . Suppose we have a coordinate transformation that takes ${ g }_{ m n }^{ ' }\left( y\right) \rightarrow { g }_{ m n }\left( x\right)$ such that ${ g }_{ m n }\left( X\right) ={ \delta }_{ m n }$ for a particular point $x=X$ . Susskind wants to show that, in general, the first derivatives, ${ \partial }_{ r }{ g }_{ m n }\left( x\right)$ , can be chosen to be zero, but the
Cites Daniel Mahler · 2015-11 · Physics Stack Exchange · on “Curvature of Conical spacetime”
Here is a purely geometrical way to think about this Edward says it is possible to cut a wedge out of a flat spacetime and glue the edges together. So in my mind this looks like a paper cone. A cone is flat precisely because it can be created by rolling up a flat sheet. Rolling up preserves the metric on the interior of the sheet (not on the boundaries where the wedge was cut out). Changing the metric requires stretching or topological changes. Rolling up does not involve stretching. Therefore the intrinsic geometry of the cone is defined to be the geometry of the flat sheet except at the seam. Since a cone has rotational symmetry this implies it is flat everywhere except the tip. The tip is
Cites user288251 · 2021-02 · Physics Stack Exchange · on “How do you Describe a Geometry where the Christoffel Symbols Vanish?”
Consider a curved space. In geodesic coordinates , the Christoffel symbols vanish, at a point , although the derivatives of those symbols do not vanish . (d'Inverno. Introducing Einstein's Relativity. page 77-78) I've been using the term "Locally flat" to describe a geometry where the Christoff Symbols can be ignored, The Christoffel symbols can be non-0 in flat space. Consider polar coordinates. Polar coordinates are flat. Christoffel symbols alone are not a measure of flatness of a space. The measure of curvature is The Riemann Tensor. $\Gamma= 0$ everywhere $\implies {R^a}_{bcd}=0$ (d'Inverno. page 80) $\Gamma= 0$ at a point $\implies {R^a}_{bcd}=$ something that involves only derivatives
Cites Berni Waterman · 2025-08 · Physics Stack Exchange · on “Susskind's covariant derivative”
Recently, I've been trying to get a better understanding on general relativity. As a non-physicist with a good mathematics background, I picked up on Susskind's course on general relativity (which is available as either a book [LINK] or a free lecture online [this video] ), which is specifically targeted at people like me. Having loved all of his other "theoretical minimum" courses I've read so far (classical mechanics, special relativity and classical field theory), I was hoping that his intuitive, yet mathematically quite rigorous approach (compared to other "popular" literature) would also help me getting into one of the more difficult theories of physics in my free-time. However, I got unfort