From Rotating Attractors to Extremal Black Holes with Axionic Hair

TL;DR

The paper analyzes extremal rotating black holes in Einstein–Maxwell–axion theory by combining near-horizon geometry (NHEG) and global bulk analyses. It proves that regular rotating attractors with axionic hair exist only for purely electric or purely magnetic charges, excluding dyonic attractors both perturbatively and non-perturbatively, and shows horizon data are fixed by the entropy function when a smooth NHEG exists. The authors construct asymptotically flat, rotating extremal EMA black holes in the electric sector that interpolate to the NHEG, confirming the attractor mechanism and the decoupling of horizon data from asymptotic moduli up to a critical point $P$ where smoothness fails. These results delineate the reach and limits of NHEG-based attractor analyses in EMA and underscore the crucial role of the axion-photon coupling in determining horizon physics.

Abstract

We study extremal, rotating black holes in four-dimensional Einstein-Maxwell-axion (EMA) theory through a combined near-horizon and bulk analysis. At the level of the near-horizon extremal geometry (NHEG), using the entropy function formalism, we prove that regular rotating attractors with axionic hair exist only for configurations that are purely electrically or purely magnetically charged; regular rotating dyonic attractors are excluded by the axion equation of motion, a result that we established perturbatively and non-perturbatively within the NHEG system. On the global side, we construct families of asymptotically flat, rotating extremal EMA black holes that interpolate to the electric NHEG branch, confirming that horizon data are fixed by extremization of the entropy function and decoupled from asymptotic moduli in line with the attractor mechanism.

Figures (5)

• Figure 1: The profile of a typical rotating near-horizon solution with $g_{_{\psi\gamma\gamma}}=1$
• Figure 2: A comparison between the results for extremal black hole (dashed) solutions (blue curve) and near-horizon configurations (red smooth curve). The two curves coincide up to the critical configuration $P$. Beyond $P$, the bulk solutions extending into a set of non-smooth configurations (black dotted curve) for $g_{_{\psi\gamma\gamma}}=1$ and $g_{_{\psi\gamma\gamma}}=\sqrt{\frac{3}{2}}$ in the insets.
• Figure 3: (Left Panel) The reduced Kretschmann scalar curves, with constant electric potential on the horizon, as a function of the temperature. (Right Panel) The reduced Ricci scalar curves, with constant electric potential on the horizon, as a function of the temperature (color code used for the legend is given on the Left Panel). In the inset, a zoomed-in visualization of the curve with constant $\Phi_{\mathcal{H}}=0.1$.
• Figure 4: Some quantities of interest are shown for bulk extremal black hole solutions.
• Figure 5: Profile functions of a typical extremal solution with $g_{_{\psi\gamma\gamma}}=1$, $r_H=0.10$, $\Omega_H=1.0$, $\Phi_{\mathcal{H}}=0.40$, $vs.$ the compactified radial coordinate $1-r_H/r$, for several different polar angles $\theta$. The insets show the corresponding functions for a solution with $g_{_{\psi\gamma\gamma}}=\sqrt{\frac{3}{2}}$ with the same input parameters $\{r_H,\Omega_H,\Phi_{\mathcal{H}} \}$.