In magnetostatic the continuity equation is: $$\frac {\partial \rho}{\partial t} + \nabla \vec j(\vec r)=0$$. In my script the following is said: Since we are in magnetostatic $\frac {\partial \rho}{\partial t} =0$ and therefore $\nabla \vec j(\vec r)=0$. Now I understand that this $\nabla \vec ...

Grothendieck once asked "What is a meter?" (https://golem.ph.utexas.edu/category/2006/08/letter_from_grothendieck.html). This innocent sounding question, made me to think about how coordinate systems are defined in physics. How are coordinate systems in physics defined, for example in special re...

I'm given a metric $$ds^2=g_{\mu\nu}dx^\mu dx^\nu=\left(1-\frac{r_g}{r}\right)c^2dt^2-\left(1+\frac{r_g}{r}\right)dr^2-r^2d\theta^2-r^2\sin^2\theta d\phi^2$$ where $r_g$ is a constant. The torsion tensor is $$T^k_{ij}\equiv \Gamma^k_{ij}-\Gamma^k_{ji}.$$ But the formula that I'm using that is $$\...