The stability of regular black holes and other compact objects with a charged de Sitter core and a surface matter layer.

The stability and other physical properties of a class of regular black holes, quasiblack holes, and other electrically charged compact objects are investigated in the present work. The compact objects are obtained by solving the Einstein-Maxwell system of equations assuming spherical symmetry in a static spacetime. The spacetime is split in two regions by a spherical surface of coordinate radius $a$. The interior region contains a non-isotropic charged fluid with a de-Sitter type equation of state, $p_r = -\rho_m$, $p_r$ and $\rho_m$ being respectively the radial pressure and the energy density of the fluid. The charge distribution is chosen as a well behaved power-law function. The exterior region is the electrovacuum Reissner-Nordstrom metric, which is joined to the interior metric through a spherical shell (a matter layer) placed at the radius $a$. The matter of the shell is assumed to be a perfect fluid satisfying a linear barotropic equation of state, ${\cal P}=\omega\sigma$, with ${\cal P}$ and $\sigma$ being respectively the pressure and energy density of the shell, and $\omega$ is a constant. The exact solutions obtained are analyzed in some detail, and this is the first important contribution of this work. The stability of the solutions are then investigated considering perturbations around the equilibrium position of the shell. This is the second and the most important contribution of this work, complementing the previous studies. We find that there are stable objects in relatively large regions of the parameter space. In particular, there are stable regular black holes for all values of the parameter $\omega$ of interest. Other stable ultra-compact objects as quasiblack holes, gravastars, and even overcharged stars are allowed in certain regions of the parameter space.