This is more of a rant than anything else, but I need to, and if anybody wants to answer you're welcome. So the thing is, I guess like pretty much everybody studying physics, when I was younger, like in high school or so, I was always between the best students. During the first years in physics I...

$3$-branes are special in the following sense: only for $p=3$, the black p-brane solution admits a constant dilaton, while it is running for $p\not=3$. In particular, the dilaton $\phi$ diverges at the horizon of extremal $p$-brane solutions for $p\not=3$, which means that the string coupling $g_...

Here is an answer to the question of why the $AdS_5\times S^5$ metric is appearing. This is taken almost directly from the TASI lectures I cite at the end. If you consider N coincident Dp-branes, the background solution has a metric and dilaton which we can write as $$ds^2 = H^{-1/2}(r)\left[-f(...

In the way you interpreted the problem, you will not only find 3 solutions, but an infinite number of them. This is because the friction can take any value between 0 and $\mu N$ in both directions. The way I interpret the problem though, is that the force is the minimal force necessary to prev...