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Register a new userKerr-Newman-AdS Black Hole Surrounded by Perfect Fluid Matter in Rastall Gravity
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The Rastall gravity is the modified Einstein general relativity, in which the energy-momentum conservation law is generalized to $T^{mu u}_{~~;mu}=lambda R^{, u}$. In this work, we derive the Kerr-Newman-AdS (KN-AdS) black hole solutions surrounded by the perfect fluid matter in the Rastall gravity using the Newman-Janis method and Mathematica package. We then discuss the black hole properties surrounded by two kinds of specific perfect fluid matter, the dark energy ($omega=-2/3$) and the perfect fluid dark matter ($omega=-1/3$). Firstly, the Rastall parameter $kappalambda$ could be constrained by the weak energy condition and strong energy condition. Secondly, by analyzing the number of roots in the horizon equation, we get the range of the perfect fluid matter intensity $alpha$, which depends on the black hole mass $M$ and the Rastall parameter $kappalambda$. Thirdly, we study the influence of the perfect fluid dark matter and dark energy on the ergosphere. We find that the perfect fluid dark matter has significant effects on the ergosphere size, while the dark energy has smaller effects. Finally, we find that the perfect fluid matter does not change the singularity of the black hole. Furthermore, we investigate the rotation velocity in the equatorial plane for the KN-AdS black hole with dark energy and perfect fluid dark matter. We propose that the rotation curve diversity in Low Surface Brightness galaxies could be explained in the framework of the Rastall gravity when both the perfect fluid dark matter halo and the baryon disk are taken into account.
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We obtain the Kerr-anti-de-sitter (Kerr-AdS) and Kerr-de-sitter (Kerr-dS) black hole (BH) solutions to the Einstein field equation in the perfect fluid dark matter background using the Newman-Janis method and Mathematica package. We discuss in detail the black hole properties and obtain the following main results: (i) From the horizon equation $g_{rr}=0$, we derive the relation between the perfect fluid dark matter parameter $alpha$ and the cosmological constant $Lambda$ when the cosmological horizon $r_{Lambda}$ exists. For $Lambda=0$, we find that $alpha$ is in the range $0<alpha<2M$ for $alpha>0$ and $-7.18M<alpha<0$ for $alpha<0$. For positive cosmological constant $Lambda$ (Kerr-AdS BH), $alpha_{max}$ decreases if $alpha>0$, and $alpha_{min}$ increases if $alpha<0$. For negative cosmological constant $-Lambda$ (Kerr-dS BH), $alpha_{max}$ increases if $alpha>0$ and $alpha_{min}$ decreases if $alpha<0$; (ii) An ergosphere exists between the event horizon and the outer static limit surface. The size of the ergosphere evolves oppositely for $alpha>0$ and $alpha<0$, while decreasing with the increasing $midalphamid$. When there is sufficient dark matter around the black hole, the black hole spacetime changes remarkably; (iii) The singularity of these black holes is the same as that of rotational black holes. In addition, we study the geodesic motion using the Hamilton-Jacobi formalism and find that when $alpha$ is in the above ranges for $Lambda=0$, stable orbits exist. Furthermore, the rotational velocity of the black hole in the equatorial plane has different behaviour for different $alpha$ and the black hole spin $a$. It is asymptotically flat and independent of $alpha$ if $alpha>0$ while is asymptotically flat only when $alpha$ is close to zero if $alpha<0$.
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