  We study the linear stability of a nongravitating, steady-state, spherically
symmetric ghost condensate accreting onto a Schwarzschild black hole using two
methods. The first one is based on the conservation of the energy-momentum
tensor of the perturbations (whose propagation is determined by the effective
metric), and involves the determination of the sign of the time derivative of
the energy of the perturbations. The second method employs the positivity of
the effective potential. Both methods yield the result that the system is
stable, but the second one is less practical, since it involves lengthier
calculations and requires the explicit form of the background solution for the
scalar field.

General Relativity and Quantum Cosmology