Charged rotating noncommutative black holes

In this paper we complete the program of the noncomutative geometry inspired black holes, providing the richest possible solution, endowed with mass, charge and angular momentum. After providing a prescription for employing the Newman-Janis algorithm in the case of nonvanishing stress tensors, we find regular axisymmetric charged black holes in the presence of a minimal length. We study also the new thermodynamics and we determine the corresponding higher-dimensional solutions. As a conclusion we make some consideration about possible applications.

Figure 1

Plot of the surface gravity as a function of the horizon radius for different values of the $a$. The rotation has just the effect of increasing the values of the mass of the black hole remnant.

Figure 2

Plot of the function $\Delta =0$ for the neutral rotating case. The parameter $a$ is along the $z$-axis there, the horizon radius is along the $x$-axis, and the mass $M$ is along the $y$-axis. Qualitatively this is the behaviors of the rotating charges solution too.

Figure 3

Plot of the Ricci scalar as a function or $r$ and $\vartheta$ for different values of the couple $(M,a)$. Along the equatorial plane, i.e. $\vartheta =\pi /2\sim 1.57$ the de Sitter belt appears. For all other angles, one finds a flat disk, i.e., vanishing curvature.