= Hedgehog monopole equations in radial profile variables
{title2=$K'=-fK,\quad f'=(1-K^2)/r^2$}
For $\Phi^a=f(r)x^a/r$ and $A_i^a=\epsilon_{iaj}x^j\alpha(r)$ with $[e_a,e_b]=\epsilon_{abc}e_c$, set $K=1+r^2\alpha$. The equation $B=-D\Phi$ equates radial coefficients to give $f'=-2\alpha-r^2\alpha^2$ and transverse coefficients to give $r\alpha'+2\alpha=-f/r-r\alpha f$. These are exactly the displayed two radial equations. The sign depends on the chosen orientation and on the order of indices in the gauge ansatz.
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