Stability of horizon in warped AdS black hole via particle absorption

We investigate the stability of the horizon in a warped anti-de Sitter black hole based on three-dimensional new massive gravity due to particle absorption. If a particle moving towards the black hole enters its outer horizon, the black hole changes because it absorbs the conserved quantities of the particle. This variation is constrained by the equations of motion of the particle. We prove both the irreducibility of the entropy and the stability of the horizon for the black hole through this process. However, horizon instability is found for a near-extremal black hole by considering its second-order expansion. We resolve this instability by applying an adiabatic process for the absorption. Furthermore, we show that the stability has a physical counterpart in the eigenvalue of the energy spectrum of the Virasoro generator via a warped anti-de Sitter/warped conformal field theory correspondence.