Abstract
Dynamics of charged rotating BTZ black holes in 2 + 1 dimensions by using the cut and paste approach is discussed. Due to the mechanical stability of rotating charged BTZ thin shell, the radial perturbation about the equilibrium throat radius and three variable equation of state (EoS) is analyzed. Several examples are displayed satisfying it, such as variable Phantom-like, variable Chaplygin gas and variable modified generalized Chaplygin gas.