A question about cheese magically attracts the TikZmice. They are part of a LaTeX package named "tikzlings" which is currently developed with the help many TeX.Stackexchange users. In case you want to try it yourself, the package source code is available from https://github.com/samcarter/tikzli...

As i can remember, for the case of classical electrodynamic the d.o.f counting start after the assumption of the Bianchi Identity, and at the end the desired result came all from the gauge freedom. In fact $\partial_{[\mu}F_{\nu\alpha]}=0$ only choose a suitable form for $F_{\mu\nu}$, for example...

I'm confused about the number of degrees of freedom in General Relatity. There are two ways to count it. However, they are contradictory. For simplicity, we consider vacuum solution. First, $G_{\mu\nu}=0$ gives $10$ equations and $g_{\mu\nu}$ have $10$ degrees of freedom(d.o.f). While $\nabla^\m...

The key point in all of this is that general relativity is a gauge theory, and, as the saying goes, "the gauge always hits twice" (apparently attributed to Claudio Teitelboim). What this means is that (1) you have an arbitrary freedom in defining your evolution, corresponding to the ability to m...

The $4\times 4$ tensor is symmetric, so the $6$ entries below the leading diagonal are equal to the $6$ above it. Therefore, there are only $4^2-6=4+6=10$ DOFs before we consider Bianchi; the sum $4+6$, another way of counting the DOFs, is one triangle plus a diagonal. Bianchi is a vector$=0$ con...