Numerical study of instability of fluid black holes

Recently neutral and charged black-hole solutions were found for static perfect fluid with the equation of state $$p(r)=-\rho (r)/3$$ , for fluid only as well as for fluid in the presence of electric field. In those works, the stability of the black holes were studied in an analytic manner, which concluded that the black holes are unconditionally unstable. In this work, we focus particularly on the numerical study of the instability. For the black-hole solutions as well as the static solutions without horizons, we solve the perturbation equations numerically and find the unstable mode functions.