Dirac Quasinormal Modes of a Schwarzschild Black Hole surrounded by Free Static Spherically Symmetric Quintessence

We evaluate the quasinormal modes of massless Dirac perturbation in a Schwarzschild black hole surrounded by the free static spherically symmetric quintessence using the third-order Wentzel-Kramers- Brillouin (WKB) approximation. The result shows that the massless Dirac field damps more slowly due to the presence of quintessence. The real part of the quasinormal modes increases and the absolute value of the imaginary part increases when the state parameter w(q). increases. In other words, the massless Dirac field decays more rapidly for the larger w(q.). The peak value of potential barrier becomes higher as vertical bar k vertical bar increases and the location of peak moves along the right for fixed w(q).