New solutions of charged regular black holes and their stability

We construct new regular black hole solutions by matching the de Sitter solution and the Reissner-Nordstr\"om solution with a timelike thin shell. The thin shell is assumed to have mass but no pressure and obeys an equation of motion derived from Israel's junction conditions. By investigating the equation of motion for the shell, we obtain stationary solutions of charged regular black holes and examine stability of the solutions. Stationary solutions are found in limited ranges of $0.87L\ensuremath{\le}m\ensuremath{\le}1.99L$, and they are stable against small radial displacement of the shell with fixed values of $m$, $M$, and $Q$ if $M>0$, where $L$ is the de Sitter horizon radius, $m$ the black hole mass, $M$ the proper mass of the shell, and $Q$ the black hole charge. All the solutions obtained are highly charged in the sense of $Q/m>2\sqrt{3}\ensuremath{\approx}0.866$. By taking the massless limit of the shell in the present regular black hole solutions, we obtain the charged regular black hole with a massless shell obtained by Lemos and Zanchin and investigate stability of the solutions. It is found that Lemos and Zanchin's regular black hole solutions given by the massless limit of the present regular black hole solutions permit stable solutions, which are obtained by the limit of $M\ensuremath{\rightarrow}0$.