## 5 Conclusions  
An additional homothetic (self-similar) symmetry to space-time was assumed, and nonstatic solutions for the electromagnetic system with added gravity (Einstein-Maxwell systems) are obtained in a simple form. Coupling with the outer Reissner-Norstrom-Vaidya space-time and using it as a transport mechanism, the radiation flux freely escapes from the distribution.  
It has been demonstrated, once again, as well as matter can be considered as an anisotropic fluid, when it is electrically charged. The approach is achieved by obtaining a dynamical model by means of the free escape approximation and self-similarity within the source. It is represented in the chosen example by manipulating only the initial conditions \(k\), \(l\), and CT and setting physical conditions: \(-1<\omega<1\), \(p<\rho\,y\,\rho>0\). A considerable set of initial conditions was selected for several runs of the programs, verifying the results shown. Several solutions were discarded, as they did not meet the above energy conditions.  
More general solutions of the symmetry equations are needed to explore the generality of the results shown in this paper. Nevertheless, the anisotropic approach employed  
Figure 6: Radiation flux (multiplied by \(10^{2}\)).  
Figure 7: The changes are shown for different layers of the matter distribution.  
achieves results that are in agreement with those reported in other previously published work and which conclude that the final state is the steady-state [18].  
An important feature is the anisotropy factor \(p_{r}-p_{t}=2\mu\), where it is clear that the loading induces anisotropy. If the charge is zero, of course, the anisotropy factor is zero. This fact was used as a way to validate the code, because results for zero charges have been reported previously. Figure 3 shows the radius of the distribution, which collapses inexorably. Unlike [2; 13; 18; 42; 43], the electric charge does not stop the collapse.  
In theory, while a black hole can possess a very large charge, the charge of the newly detected holes will be considered negligible. This assumption is based on the fact that a black hole is always surrounded by plasma. With the self-similar solutions proposed in this work, new models of black hole formation can be considered and also verify that the electric charge in the formation of a black hole can be significant. Models already reported establishing that, although the charge of a black hole is large, the charge/mass ratio is small and is not enough to significantly affect either the gravitational field of the matter distribution or the dynamics of the star or its collapse [44; 45; 46; 47; 48; 49; 50; 51; 52; 53].  
Conceptualization, F.S.-C. and L.R.-R.; methodology, F.S.-C. and L.R.-R.; investigation, F.S.-C. and L.R.-R.; writing--original draft preparation L.R.-R.; writing--review and editing F.S.-C.; supervision, F.S.-C. and L.R.-R.; project administration, F.S.-C. and L.R.-R. All authors have read and agreed to the published version of the manuscript.  
This research was funded by La Universidad de Las Americas-Ecuador and Universidad Politecnica de Venezuela, Puerto Ordaz.  
Not applicable.  
The authors declare no conflict of interest.