From Rotating Attractors to Extremal Black Holes with Axionic Hair

TL;DR

This paper investigates extremal rotating black holes with axionic hair in Einstein-Maxwell-axion theory, showing that regular attractors are purely electric or magnetic, and constructing asymptotically flat solutions consistent with the attractor mechanism.

Contribution

It demonstrates that regular rotating attractors with axionic hair are limited to purely electric or magnetic types and constructs explicit solutions confirming the attractor behavior.

Findings

Regular rotating attractors with axionic hair are purely electric or magnetic.

Dyonic attractors are excluded by the axion equation of motion.

Constructed asymptotically flat extremal black holes matching near-horizon data.

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.