Late-time evolution of Dirac field around Schwarzschild-quintessence black hole

The late-time evolution of Dirac field around spherically symmetric black hole surrounded by quintessece is studied numerically. Our results show, for lower values of the quintessence state parameter ε, Dirac field decays as power-law tail but with a slower decay rate than the corresponding Schwarzschild case. But for ε<-1/3, all the \ell-poles of the Dirac field give up the power-law decay form and relax to a constant residual field at asymptotically late times. The value of this residual field for which the field settles down varies on different surfaces. It has the lowest value on the black hole event horizon, increases as the radial distance increases and maximizes on the cosmological horizon.

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