B. Stability of the shell against single particle decay

In this section we discuss the stability of the trajectory of the infinitesimally thin shell under single particle decay, following the treatment that can be found in [8]. The proof that the shell is stable against single particle decay of uncharged particles is not reproduced here, because it can be easily derived from the reference cited above, to which the reader is referred. We will instead shortly discuss the case in which charged particles are involved.

In more detail, the relevant question is if the motion of a charged particle, which at the instant of maximum expansion starts out where the shell is located, will subsequently be governed by a confining, i.e. ``$\cup$-shaped'', effective potential, or not. Performing the analysis at the instant of maximum expansion, where the potential is static, simplifies the computation: subsequent changes of the potential will have, anyway, only adiabatic effects on the locally trapped particle and this is not relevant for the point under discussion. To get the desired result we will proceed in two steps:

1. identify the effective potential governing the motion of a particle in the exterior Reißner-Nordström geometry;
2. evaluate if it is ``$\cup$-'' or ``$\cap$-shaped'' at the point of maximum expansion.

We will work in the adimensional units used throughout the rest of the paper.