Spinning-charged-hairy black holes in 5D Einstein gravity

The spinning-hairy black holes that occur in Einstein’s gravity, supplemented by a doublet of complex scalar fields, are constructed within an extension of the model by a U(1) gauge symmetry involving a massless vector potential. The hairy black holes then acquire an electric charge and a magnetic moment; their domain of existence is discussed in terms of the gauge coupling constant.

Figure 1

(Left) Mass-frequency relation for boson star solutions (red line) for hairy black holes with three values of $r_H=0.3$, 0.4, 0.65 (black lines) and for extremal solutions (blue line). (Right) Sketch of the domains of Myers-Perry and hairy black holes in the ${\mathrm{\Omega }}_H\text{−}M$ plane.

Figure 2

(Left) Several quantities characterizing the black holes for $q=0$ as functions of the parameter $A_H$. (Right) The mass $M$ and electric potential $V_0$ as function of $q$ for the solutions corresponding to $A_H=0.0$ and $A_H=-0.1$.

Figure 3

(Left) The combination $\mu -|\omega -q{V}_0|$ as a function of $q$ for several values of $A_H\le 0$. (Right) The temperature for the same set of solutions. Both plots are realized for ${\mathrm{\Omega }}_H=0.967$ and $r_H=0.3$.

Figure 4

(Left) The scalar (black) and vector (red) energy density for $q=0$ (dot-dashed) and for $q=0.4$ (solid) for $A_H=0$. (Right) The same for $A_H=-0.14$. On both sides the dot-dashed curve is the same, allowing the reader to compare the plots. Both plots are realized for $r_H=0.3$ and ${\mathrm{\Omega }}_H=0.967$.

Figure 5

(Left) Profile of the magnetic potential $A$ with $A_H=-0.1$ for $q=0.1$, 0.3, 0.5, 0.55, 0.57, and $0.575\approx q_{\max }$, respectively, in black, red, orange, yellow, green, and blue. These curves are for ${\mathrm{\Omega }}_H=0.967$ and $r_H=0.3$. (Right) The same for the scalar function $F$.