Stability of the accretion of a ghost condensate onto the Schwarzschild black hole

Claudia A. Rivasplata Paz, Jose Martins Salim, Santiago Esteban Perez Bergliaffa

Published 2014-03-19Version 1

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.