# Samalkhaiat's challenge #001

## Main Question or Discussion Point

Heh, heh, you should write a "Theoretical Physics Challenge" thread, similar to the "Math Challenges". Heh heh, unfortunately I can’t do that. However, many of my posts in here do (sometimes) contain exercises. I will try to make it a habit in the future. Here is one relevant for relativity forum:
Use the definition $$T^{\mu\nu} = \frac{1}{\sqrt{-g}} \frac{\delta (\sqrt{-g}\mathcal{L})}{\delta g_{\mu\nu}} ,$$ to show that $$T^{\mu\nu} = V^{\mu}V^{\nu} (\rho - p) - g^{\mu\nu}p ,$$ is derivable from the Lagrangian $$\mathcal{L} = 2 \sigma (x) \left(1 + \pi (\sigma) \right) ,$$ where $\sigma (x)$ is the density of an isotropic fluid in some space-time region, and $\pi (\sigma)$ is the potential energy per unit density $\sigma$, i.e., the elastic potential of the fluid.

I think the solution is in Pauli's lectures on QFT
Are these in English?
or also in Bogoliubov&Shirkov.
I learnt QED from that book. In my opinion, it is the best book ever written on QED. I still use it whenever I get stuck on something.

• vanhees71 and JD_PM

Related Special and General Relativity News on Phys.org
strangerep
However, many of my posts in here do (sometimes) contain exercises. I will try to make it a habit in the future. I've asked the moderators to move this exercise into its own "challenge" thread. • 