Numerical Study of Instability of Fluid Black Holes

TL;DR

This paper conducts a numerical analysis of fluid black hole instabilities, confirming their unconditional instability through solving perturbation equations for both black-hole and horizonless solutions.

Contribution

It provides the first detailed numerical study of the instability modes of fluid black holes, complementing previous analytic results.

Findings

Unstable mode functions identified numerically

Confirms unconditional instability of fluid black holes

Analyzes both black-hole and horizonless solutions

Abstract

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 {\it 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.