A new rotating axionic AdS$_4$ black hole dressed with a scalar field

Abstract

This paper presents a new four-dimensional axionically charged rotating black hole with a scalar field, which is defined by a structural function coupling the axionic field and a scalar potential. This configuration is characterized by an integration constant and two constant parameters. The thermodynamic quantities are obtained via the Euclidean procedure, where the validity of the first law of thermodynamics is ensured. These results indicate that the rotating configuration provides a useful framework for exploring holographic superconductors, where the angular constant parameter plays a central role.

Figures (3)

• Figure 1: Left Panel: Graphical representation of ${\ell^2 f(r)}/{r^{2}}$ as a function of the radial coordinate $r$, with $\eta=B=\ell=1$ for our calculations. Here, Case I (red dotted curve), characterized by $\alpha=1$, indicates the presence of a naked singularity ($4-{\ell^2 \eta^2/\alpha}>0$). Case II (black curve) corresponds to the extremal case, given by $\alpha=1/4$. Here, ${\ell^2 f(r^{*})}/{(r^{*})^{2}}=({\ell^2 f(r^{*})}/{(r^{*})^{2}})'=0$ and this condition emerges when $4-{\ell^2 \eta^2/\alpha}=0$. Finally, Case III (dashed blue curve and when $\alpha=1/9$) reveals the situation where $4-{\ell^2 \eta^2/\alpha}<0$. Right Panel: Graphical representation of the increasing function ${\ell^2 f(r)}/{r^{2}}$ at the limit $\alpha \rightarrow 0^{+}$, with $\eta=B=\ell=1$, through the black dotted dashed curve. Here, the location of the event horizon is ensured.
• Figure 2: The condensation profiles for the operators $\mathcal{O}_1$ and $\mathcal{O}_2$ as a function of temperature, considering different values of the rotation parameter $\alpha$. The continuous (black) curve corresponds to the static case, while the dashed (violet), dot-dashed (blue), and dotted (red) curves correspond to situations with non-zero rotation.
• Figure 3: The $\sigma_{\tiny{\hbox{DC}}}$ curve for the real (left panel) and imaginary (right panel) parts of the electrical conductivity for different values of the rotation parameter $\alpha$. The continuous (black) curve corresponds to the static case, while the other values correspond to situations with non-zero angular momentum.