Charged black holes by gravitational decoupling satisfying a non-local EoS

In this work, we have constructed solutions for charged black holes through gravitational decoupling, using the Reissner–Nordstrom solution as a seed. As an additional condition to close the system, we have considered a non-local equation of state for the decoupler sector. As a result, our solutions possess the same event horizon as the Reissner–Nordstrom seed solution and depend on a free parameter, which happens to be the gravitational decoupling parameter, interpreted as a generic hair of the solution. It is demonstrated that for certain parameter values in the parameter space, the solution satisfies all energy conditions outside the event horizon. Furthermore, our solution does not contain extra singularities besides the already known essential singularity at r=0 of the seed solution. To comprehend the behavior of test particles around our solution, potentially useful for comparison with observational data, we have conducted geodesic analysis for massive particles. Particularly, we find that the decoupling parameter plays a fundamental role in the periastron advance, as it increases, the advance angle grows. To complete the discussion, we have studied the quasinormal modes using the high-order WKB method, considering scalar, vector, and tensor perturbations (axial and polar). We find that once again, the decoupling parameter affects the frequency of the quasi-normal modes. Specifically, as it increases, the imaginary part becomes increasingly negative, indicating a greater damping of the signal. Finally, we found that generic hair breaks the isospectrality of the seed solution.