Kerr-Newman-AdS black hole in quintessential dark energy

Quintessential dark energy with pressure $p$ and density $\rho$ 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 $\mathrm{\Lambda }$ 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 $\mathrm{\Lambda }$ to 1. When $\omega \to -1$, 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.

Figure 1

Two pictures show the behavior of $a^2+Q^2-{\mathrm{\Delta }}_r$ with $r$ for fixed $M=1$, in which for different $\omega$, $\alpha$ will satisfy different value when the cosmological horizon exists. Due to the small value of the cosmological constant, there always exists the cosmological horizon $r_c$.

Figure 2

The shape of ergosphere of the Kerr-Newman-AdS black hole in quintessence for different $a,Q(=q),\alpha$ and $\omega =-2/3$. The blue lines represent event horizons and red lines represent stationary limit surfaces. The region between event horizon and stationary limit surface is the ergosphere. Because the cosmological constant is small, its influence can be ignored. Here $\mathrm{\Lambda }=1.3\times {10}^{-56}{\mathrm{cm}}^{-2}$.

Figure 3

The behavior of rotation velocity $v$ with $r$ in the equatorial plane of the Kerr-Newman-AdS black hole in quintessential dark energy for two examples $\omega =-1/2$ and $\omega =-2/3$. The top panels show the curves for different parameter $a$: solid line $a=0$, dashed line $a=0.3$, dot-dashed line $a=0.6$ and dotted line $a=0.9$. The bottom panels present the curves for different parameter $Q$: solid line $Q=0$, dashed line $Q=0.3$, dot-dashed line $Q=0.6$ and dotted line $Q=0.9$. Here $\mathrm{\Lambda }={10}^{-56}c{m}^{-2}$ and $\alpha =0.0005$.

Figure 4

The behavior of rotation velocity $v$ with $r$ in the equatorial plane of the Kerr-Newman-AdS black hole in quintessential dark energy for two examples $\omega =-1/2$ and $\omega =-2/3$. The top panels show the curves for different parameter $a$: solid line $a=0$, dashed line $a=0.3$, dot-dashed line $a=0.6$ and dotted line $a=0.9$. The bottom panels present the curves for different parameter $Q$: solid line $Q=0$, dashed line $Q=0.3$, dot-dashed line $Q=0.6$ and dotted line $Q=0.9$. Here $\mathrm{\Lambda }={10}^{-56}{\mathrm{cm}}^{-2}$ and $\alpha =5*{10}^{-10}$.

Figure 5

The behavior of rotation velocity $v$ with $r$ in the equatorial plane of the Kerr-Newman-AdS black hole in quintessential dark energy. The left picture show the curves for different parameter $a$: solid line $a=0$, dashed line $a=0.3$, dot-dashed line $a=0.6$ and dotted line $a=0.9$. The right picture present the curves for different parameter $Q$: solid line $Q=0$, dashed line $Q=0.3$, dot-dashed line $Q=0.6$ and dotted line $Q=0.9$. Here $\mathrm{\Lambda }={10}^{-56}{\mathrm{cm}}^{-2}$ and $\omega =-1/3$.