Kerr-Newman-AdS black hole in quintessential dark energy

Quintessential dark energy with pressure rho and density. is related by equation of state p =omega rho with the state parameter - 1 < omega < -1/3. The cosmological dark energy influence on black hole spacetime is interesting and important. In this paper, we study the Kerr-Newman-AdS solutions of the Einstein-Maxwell equation in quintessence field around a black hole by Newman-Janis algorithm and complex computations. From the horizon structure equation, we obtain the expression between quintessence parameter alpha and cosmological constant Lambda if the black hole exists two cosmological horizon r(q) and r(c) when omega = -2/3, the result is different from rotational black hole in quintessence matter situation. Through analysis we find that the black hole charge cannot change the value of alpha. But the black hole spin and cosmological constant are opposite. The black hole spin and cosmological constant make the maximum value of alpha small. The existence of four horizon leads seven types of extremal black holes to constrain the parameter alpha. With the state parameter omega ranging from -1 to - 1/3, the maximum value of alpha changes from Lambda to 1. When omega -> -1, the quintessential dark energy likes cosmological constant. The singularity of the black holes is the same with that of Kerr black hole. We also discuss the rotation velocity of the black holes on the equatorial plane for omega= - 2/3, - 1/2 and - 1/3. For small value of alpha, the rotation velocity on the equatorial plane is asymptotically flat and it can explain the rotation curves in spiral galaxies.