Quasinormal modes of a black hole surrounded by quintessence

Abstract

Using the third-order WKB approximation, we evaluate the quasinormal frequencies of massless scalar field perturbation around the black hole which is surrounded by the static and spherically symmetric quintessence. Our result shows that due to the presence of quintessence, the scalar field damps more rapidly. Moreover, we also note that the quintessential state parameter $ε$ (the ratio of pressure $p_q$ to the energy density $ρ_q$) play an important role for the quasinormal frequencies. As the state parameter $ε$ increases the real part increases and the absolute value of the imaginary part decreases. This means that the scalar field decays more slowly in the larger $ε$ quintessence case.