# Linear Stability of Mandal-Sengupta-Wadia Black Holes

## TL;DR

This paper investigates the linear stability of non-extremal Mandal-Sengupta-Wadia black holes in (2+1)-dimensional gravity, demonstrating their stability against small, circularly symmetric perturbations through a Schrödinger-like analysis.

## Contribution

It provides the first stability analysis of non-extremal MSW black holes using linear perturbation theory and Schrödinger-like equations.

## Key findings

- MSW black holes are stable against small perturbations
- Effective potential analysis confirms stability
- Results apply to non-extremal configurations only

## Abstract

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