It's differential geometry, a truly evil subject; those dreaded Christoffel symbols are instantly recognizable. I can spot the fundamental theorem of Riemannian geometry (Riemann-Christoffel formula), the Riemann curvature tensor, and the differential equation for a geodesic (where is Gauss's Theorema Egregium?).
freefunctor said: It's differential geometry, a truly evil subject; those dreaded Christoffel symbols are instantly recognizable. I can spot the fundamental theorem of Riemannian geometry (Riemann-Christoffel formula), the Riemann curvature tensor, and the differential equation for a geodesic (where is Gauss's Theorema Egregium?).
Thanks for letting me know.
I think I would expect to see some matrices for deriving the formulas. I can only recognize the Γ as a gamma function defined though an integral, though it seems generalized here. As well as the many ways of denoting a derivative (ds^2, ∂g_py/∂r^y, d^2x^μ/dt^2).
Matrices are used to perform computations more concisely, but the artist here is just listing the formulas. The Γ^ρ_μλ are the aforementioned Christoffel symbols, which express the unique torsion-free metric connection on a Riemannian manifold in local coordinates (the most important word to know here is 'manifold', then 'Riemannian manifold'). This gamma has nothing to do with the gamma function. Some of the notation can be confusing if you haven't seen differential forms before - that's the ds^2, which is the metric on the manifold, but not the other two you noted, which are just partial derivatives. The proliferation of subscripts/superscripts is a consequence of expressing everything in local coordinates, and is (not so) affectionately referred to as the 'debauch of indices'.