Anisotropic matter and nonlinear electromagnetics black holes

Abstract

It is shown that anisotropic matter black holes with two parameters $w$ and $K$ are identified as nonlinear electrodynamics (NED) black holes with power-index $s$ and charge term $ξ(s,q)$ by introducing a NED term. These NED black holes include constant scalar hair ($s=1$), charged quantum Oppenheimer-Snyder ($s=3/2$), and Einstein-Euler-Heisenberg ($s=2$) black holes derived from their known actions. Rotating NED black holes can be obtained from rotating anisotropic matter black holes when replacing $w$ and $K$ by $2s-1$ and $ξ(s,q)$. The extremal rotating NED black holes being the boundary between rotating charged NED black hole and naked singularity are derived as functions of the rotation parameter $a(q)$.

Figures (3)

• Figure 1: (a) Charge term $\xi(s,q=0.5)$ is as a function of $s$. For $0<s<\frac{3}{4}$, $\xi(s,0.5)$ increases, it blows up at $s=\frac{3}{4}$ (dashed line), and it increases negatively for $s>\frac{3}{4}$. Equation of state parameter $w(s)$ is as a function of $s$. It is negative for $0<s<\frac{1}{2}$, it is zero at $s=\frac{1}{2}$, and it is positive for $s>\frac{1}{2}$. Eight black dots are displaced for Table 1. Six red dots including one green dot (not black hole) are shown for Fig. \ref{['extremal']}(a). (b) $\xi_-(s,q=0.5)$ is as a function of $s$. Two magenta dots represent EEH and Ned black holes.
• Figure 2: Horizon structure. (a) For $s=0$ and $\xi=\frac{1}{16\pi}$, $r_\pm$ represents the outer/Cauchy horizons of Schwarzschild-de Sitter black hole for $0<M<0.471$. The dashed line is located at extremal point $M_e=0.471$. (b) For $s=1,3/2$, $\xi=\frac{1}{16\pi}$ and $M=1$. $r_\pm$ represents the outer/inner horizons of RN and cqOS black holes for $0<q<1$ and $0<q<1.53$. Two blue dots are located at extremal points (1,1) and (1.53.1.5) and they will also be displaced in Fig. \ref{['extremal']}(a).
• Figure 3: (a) Curves for extremal NED black holes with $q=0,q=0.5$ and $a=0$. All six red dots with two magenta dots shown in Figs. \ref{['xiofs']}(a) and \ref{['xiofs']}(b) are located above these extremal curves. The shaded region of asymptotically flat black holes denotes the region of $s>\frac{3}{4}(w>1/2)$. (b) Curves for extremal rotating NED black holes with $q=0,0.5$ and $a\not=0$. (c) Four curves of extremal rotating NED black holes : $a(q)=\sqrt{0.5^2-q^2},~\sqrt{0.9^2-q^2},~\sqrt{1.2^2-q^2}$, and $\sqrt{1.5^2-q^2}$. The shaded region indicates for $s>\frac{3}{4}$. Each solid curve separating the black hole (above curve) from naked singularity (below curve) are parametrically described by Eq.(\ref{['f-curves']}).