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