= Charged-particle turning-point exclusion in Reissner-Nordstrom spacetime
{title2=$\dot r=0\ \Longrightarrow\ F\ge0$}
For $0<|Q|<M$, the <charged-particle radial equation in Reissner-Nordstrom spacetime> implies that any radial <turning point> obeys
$$
F\left(1+\frac{l^2}{r^2}\right)=\frac{(E-eQ/r)^2}{m^2}\ge0.
$$
Since $1+l^2/r^2>0$, it follows that $F\ge0$. Thus no massive <test particle>, regardless of its <electric charge>, can have a radial <turning point> in $r_-<r<r_+$, where $F<0$. At a regular horizon crossing, a <timelike vector> cannot lie in the tangent space of a <null hypersurface>, so a massive particle has $\dot r\ne0$ there as well. The algebraic inequalities $r\ge r_+$ or $r\le r_-$ are necessary conditions, not an existence theorem for radial <turning points>.
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