Linear Stability of Mandal-Sengupta-Wadia Black Holes

In this letter, the linear stability of static Mandal-Sengupta-Wadia (MSW) black holes in $(2+1)$-dimensional gravity against circularly symmetric perturbations is studied. Our analysis only applies to non-extremal configurations, thus it leaves out the case of the extremal (2+1) MSW solution. The associated fields are assumed to have small perturbations in these static backgrounds. We then consider the dilaton equation and specific components of the linearized Einstein equations. The resulting effective Klein-Gordon equation is reduced to the Schr\"{o}dinger like wave equation with the associated effective potential. Finally, it is shown that MSW black holes are stable against to the small time-dependent perturbation