Charged rotating black holes in higher-dimensional (A)dS gravity

We present numerical evidences for the existence of rotating black holes in $d$-dimensional Einstein-Maxwell theory with a cosmological constant and for an odd number of dimensions. The metric used possesses $(d+1)/2$ Killing vectors and the black holes have $(d-1)/2$ equal angular momenta. The Schwarzschild-like coordinate system used clearly reveals the influence of the electromagnetic field on the vacuum black holes where analytic expressions are available. The domain of existence of the charged rotating black holes is then characterized for both signs of the cosmological constant. The generic solutions are specified by their event horizon and by two additional parameters: the magnetic field and the angular velocity at the horizon. The dependence of several physical quantities—surface gravity, mass, angular momentum, etc.—is studied as a function of these parameters; Smarr-like relations are derived.

Figure 1

The value ${\Omega }_{\max }$ and the parameter $1/{\ell }^2$ as functions of $r_c$ for the MP solution and for $r_h=0.5$, 1.0, 2.0.

Figure 2

The mass $E$, the angular momentum $J$, and the value $f_1$ as functions of $\Omega$ for the Myers-Perry solution (solid lines) and the charged solution with $A^{\prime }=0.5$ (dashed lines) for $r_h=1$ and ${\ell }^2=0.1$. The Hawking temperature $T_H$ is represented by the dotted lines.

Figure 3

Parameters of the electromagnetic field of charged AdS black holes as functions of $\Omega$ for $r_h=1$, $a_h^{\prime }=0.5$.

Figure 4

The profiles of a typical AdS rotating black hole with $r_h=1$, $\Omega =0.5$, and $a_h^{\prime }=0.5$.

Figure 5

The profiles of an extremal AdS rotating black hole with $r_h=1$, $\Omega =0.09$, and $\Lambda =-0.1$.

Figure 6

The profiles of two black hole solutions corresponding to $y_h=0.6$, $\Omega =0.33$.

Figure 7

The values $f_1$, $V_1$, and $V_{\inf }\equiv V(\infty )$ are reported as functions of $w_h$ for $a_h^{\prime }=0$, 0.1, and 0.5.

Figure 8

The values $f_1$ and $g_0$ are reported as functions of $\Omega$ for $a_h^{\prime }=0$, 0.1, and 0.5.

Figure 9

The energy of the solutions and the angular momentum $J$ are reported as functions of $\Omega$ for $a_h^{\prime }=0$, 0.1, and 0.5.

Figure 10

Electromagnetic parameters as functions of $\Omega$ for $a_h^{\prime }=0.1$ and $a_h^{\prime }=0.5$.

Figure 11

The profile of the metric and Maxwell function for $r_c=3$, $r_h=1$ for $a_h^{\prime }=0.5$ and $\Omega =0.62$.

Figure 12

The profile of the metric and Maxwell function for $r_c=3$, $r_h=1$ for $a_h^{\prime }=0.5$ and $\Omega =0.44$.